The best environment for flying creatures in our solar system may be in dense enough layers of the atmospheres of the giant planets in our solar system. If you go deep enough into the atmosphere of a giant planet you can get atmosphere as dense as you want. If in a layer where the atmosphere is about as dense as water and the animals are about as dense as water, flying should be about as easy for 10 ton animals as swimming is for 10 ton fish, 10 ton prehistoric sea reptiles, and 10 ton cetaceans.
I note that the "surface gravity" of Jupiter is 2.357 times that of Earth, Neptune's is 1.122 times, Saturn's is 0.918 times, and Uranus's is 0.887 times, so a giant planet can have a lower "surface gravity" than Earth's.
But the reason why the atmospheric density of giant planets can get as high as that of water, and many times that lower down, and the reason why "surface gravity" is within quote marks, is that giant planets don't have solid surfaces.
So nobody - whether a ground dwelling native or a human visitor - could walk on the ground and see one of those giant flying creatures swoop down on them. So if you want humans explorers to encounter giant flying creatures in the atmosphere of a giant planet, those humans will have to be in lighter than air or heavier than air flying machines, as in Arthur C. Clarke's "meeting with Medusa".
Also if there is no ground to walk on, why would the flying creatures have legs?
But it is possible for a world to have a solid surface and an atmosphere much denser than Earth's. The planet Venus has a solid surface which one space probe has landed on and which has been studied by radar. And it has a much denser atmosphere than Earth's.
The density of air or atmospheric density, denoted ρ, is the mass per unit volume of Earth's atmosphere. Air density, like air pressure, decreases with increasing altitude. It also changes with variations in atmospheric pressure, temperature and humidity. At 101.325 kPa (abs) and 20 °C (68 °F), air has a density of approximately 1.204 kg/m3 (0.0752 lb/cu ft), according to the International Standard Atmosphere (ISA). At 101.325 kPa (abs) and 15 °C (59 °F), air has a density of approximately 1.225 kg/m3 (0.0765 lb/cu ft), which is about 1⁄800 that of water, according to the International Standard Atmosphere (ISA).[citation needed] Pure liquid water is 1,000 kg/m3 (62 lb/cu ft).
https://en.wikipedia.org/wiki/Density_of_air
The atmosphere of Venus is primarily of supercritical carbon dioxide and is much denser and hotter than that of Earth. The temperature at the surface is 740 K (467 °C, 872 °F), and the pressure is 93 bar (1,350 psi), roughly the pressure found 900 m (3,000 ft) underwater on Earth.
https://en.wikipedia.org/wiki/Atmosphere_of_Venus
The atmospheric pressure at the surface of Venus is about 92 times that of the Earth, similar to the pressure found 900 m (3,000 ft) below the surface of the ocean. The atmosphere has a mass of 4.8×1020 kg, about 93 times the mass of the Earth's total atmosphere.[28] The density of the air at the surface is 65 kg/m3,[28] which is 6.5% that of liquid water on Earth.[29]
https://en.wikipedia.org/wiki/Atmosphere_of_Venus#Troposphere
So hypothetical 10 ton Venusian flying creatures which were 6.5 times as dense was water could swim in the air at the surface of Venus as well as 10 ton sea creatures swim in the oceans of Earth. And hypothetical Venusian flying creatures that were as dense as water could fly in the atmosphere at the surface of Venus about 65/1.24, or 52.4 times was well as creatures with the same mass could fly on Earth.
The ways that a planet can lose atmosphere include gases combining with other substances to become solid and precipitate onto the ground, and gases escaping into outer space.
And of course Earth, with a higher escape velocity than Venus, is more able to keep its atmosphere from escaping into space. If Earth had produced or acquired an atmosphere as massive and dense as that of Venus, it would have been even more able to retain that atmosphere for geologic eras of time than Venus. So if a planet or moon doesn't necessarily have the densest atmosphere it could possibly have, and the atmosphere it does have doesn't have to be the densest it could possibly have.
But if you want Humans to walk on the surface of your world without wearing breathing apparatus, the atmosphere will have to be thin enough for human survival.
Stephen H. Dole, in Habitable Planets for Man (1964), gives the atmospheric pressures of gases in millimeters of mercury (mmMHg).
https://www.rand.org/content/dam/rand/pubs/commercial_books/2007/RAND_CB179-1.pdf
The sea level total atmospheric pressure of all gases is about 760 mmHg.
On page 15 Dole says that an atmosphere breathable for humans must contain between about 60 mmHg of oxygen and about 400 mmHg of oxygen. On page 19 Dole says atmospheric carbon dioxide for plants should be between roughly 0.05 and 7 mmHg, and there must be some nitrogen in the air for plants.
Any planet with liquid surface water would have some water vapor in the atmosphere. Table 4 on page 21 says there is no known lower concentration of water vapor but an upper limit of 25 mmHg. But very dry air might be uncomfortable and unhealthy.
Table 3 on page 18 gives upper limits for various common toxic gases likely to be found in planetary atmospheres.
There are a number of gases which are more or less chemically inert and which can be used to dilute the oxygen in an atmosphere - within limits. Table 2 gives upper limits for such gases as known in 1964.
So the densest atmosphere possible in a human habitable world would have about 400 mmHg of Oxygen, 7 of Carbon Dioxide, 25 of Water Vapor, 160 of Xenon, 350 of Krypton, 1,220 of Argon, and 2,330 of Nitrogen, for a total pressure of 4,492 mmHg, 5.91 times the 760 mmHg of Earth's atmosphere.
Put table 2 has ? marks after the upper limits for Neon and Helium of 3,900 for Neon which would take the total up to 8,392 and 61,000 for Helium which would take the total up to 69,392 mmHg, 91,30 times the pressure of Earth's atmosphere. But the upper limits for Neon and Helium were uncertain then and might be lower today - which goes for other gases also.
Divers in non rigid suits need to have an atmospheric pressure in their lungs equal to the water pressure outside, which gets higher at deeper levels. But the atmosphere has to be a mix of gases which is not dangerous at that pressure.
Here is a link to a list of various diving mixes.
https://dive.site/blog/diving-gas-mixes/
Dole's list doesn't give a maximum pressure for hydrogen, But Dole notes that a non flammable mixture of oxygen and hydrogen must be used.
Precautions are necessary when using hydrox, since mixtures containing more than four percent of oxygen in hydrogen are explosive if ignited. Hydrogen is the lightest gas (half the weight of helium) but still has a slight narcotic potential and may cause hydrogen narcosis.4
https://en.wikipedia.org/wiki/Hydrox_(breathing_gas)
On pages 18 and 19 Dole suggests that there should a limit to atmospheric density where breathing would become exhausting. And he mentions that the flow of air at a pressure of 8 atmospheres can be felt, suggesting the limit may be near there.
So humans should be able to survive fine in the right mix of an atmosphere several times as dense as Earth's, but that might not be dense enough to make flying significantly easier for very large creatures.
Another world in our solar system with a solid system and atmosphere suitable for flying is Titan, the largest moon of Saturn.
Titan ha a mean radius of 2,574.7 kilometers (0.404 Earth) and a mass of 0.0225 Earth. It has a surface gravity of 0.138 g (0.138 Earth) and an escape velocity of 2.641 kilometers per second (0.236 Earth).
The very high ratio of atmospheric density to surface gravity also greatly reduces the wingspan needed for an aircraft to maintain lift, so much so that a human would be able to strap on wings and easily fly through Titan's atmosphere while wearing a sort of spacesuit that could be manufactured with today's technology.6
https://en.wikipedia.org/wiki/Colonization_of_Titan#Flight
And if a human could fly on Titan by attaching artificial wings to their arms and flapping, a bird or bat or flying reptile which weighed as much as a human should be able to fly very well on Titan.
The largest prehistoric flying bird on Earth was Agrentavis magnificens.
The type species, A. magnificens, is sometimes called the giant teratorn. It was among the largest flying birds ever to exist. While it is still considered the heaviest flying bird of all time, Argentavis was likely surpassed in wingspan by Pelagornis sandersi which is estimated to have possessed wings some 20% longer than Argentavis and which was described in 2014.1
Prior published weights gave Argentavis a body mass of 80 kg (180 lb), but more refined techniques show a more typical mass would likely have been 70 to 72 kg (154 to 159 lb), although weights could have varied depending on conditions.88 Argentavis retains the title of the heaviest flying bird known still by a considerable margin, for example Pelagornis weighed no more than 22 to 40 kg (49 to 88 lb).6
https://en.wikipedia.org/wiki/Argentavis
The heaviest known prehistoric flying reptile was probably Quetzcoatlus northropi.
When it was first named as a new species in 1975, scientists estimated that the largest Quetzalcoatlus fossils came from an individual with a wingspan as large as 15.9 m (52 ft). Choosing the middle of three extrapolations from the proportions of other pterosaurs gave an estimate of 11 m, 15.5 m, and 21 m, respectively (36 ft, 50.85 ft, 68.9 ft). In 1981, further advanced studies lowered these estimates to 11–12 m (36–39 ft).[11]
More recent estimates based on greater knowledge of azhdarchid proportions place its wingspan at 10–11 m (33–36 ft).8 Remains found in Texas in 1971 indicate that this pterosaur had a minimum wingspan of about 11 m (36 ft).[12] Generalized height in a bipedal stance, based on its wingspan, would have been at least 3 m (9.8 ft) high at the shoulder.4
Body mass estimates for giant azhdarchids are extremely problematic because no existing species shares a similar size or body plan, and in consequence, published results vary widely.4 Generalized weight, based on some studies that have historically found extremely low weight estimates for Quetzalcoatlus, was as low as 70 kg (150 lb) for a 10 m (32 ft 10 in) individual. A majority of estimates published since the 2000s have been substantially higher, around 200–250 kg (440–550 lb).[13][14]
If such large animals could fly on Earth, the largest animals which could fly on Titan might weigh over a ton. And it is uncertain how much over a ton an flying animal on Titan could get. Could flying animals reach 10 tons on Titan?
Nobody knows.
But obviously a world like Titan with a low surface gravity and a dense atmosphere shows the way to go. A world with lower surface gravity and denser atmosphere would be more likely than Titan to have 10 ton flying animals to go, although if humans have to breathe the air on that that world there is a limit to how dense the atmosphere can get.
Of course any known animal from Earth would need to wear protective clothing to protect it from the extremely low temperatures on Titan and breathing gear to supply oxygen to breathe.
Of course, unless you want to have lifeforms on Titan using liquid methane instead of water due to the cold, and have any humans go outside only with protective gear, you will want your world to be warm enough for liquid water using life, and probably humans, anyway.
But there is a problem. Titan is able to retain such a dense atmosphere because it is very, very cold. If it was much warmer, the gases in its exosphere would be moving much faster, and they would escape from Titan into outer space much faster.
Most of the heat on planets and moons comes from radiation from the Sun. The semimajor axis of Earth's orbit is 1 Astronomical Unit or AU by definition. The Semi-major axis of Saturn's orbit is 9.5826 AU. Which means that Titan, at the orbit of Saturn, receives only 1/(9.5826) x (9.5826), or 1/91.826,or 0.01089 01 as much radiation from the Sun as Earth gets.
Fortunately not all solar radiation is equal. The surfaces and low atmospheres of worlds are heated mostly by visible light and infrared radiation from their stars. But the gases in the exospheres of worlds, where fast moving gases escape into space, are mostly heated and speeded up by ultraviolet radiation, especially extreme ultraviolet.
So if your world orbited a cooler star, one which emitted a lot less ultraviolet radiation, there might be an orbital distance where it would get as much visible light and infrared as Earth gets, while getting no more ultraviolet than Titan gets. Such a world could have a surface temperature as high as Earth's, combined with an exosphere temperature as low as Titan's. And thus a very low gravity world in such an orbit could be able to retain a very dense atmosphere for geologic eras of time and become habitable.
Thus you might want to reconsider, and make your star a type K orang dwarf or a type M red dwarf instead of a yellow star.
And maybe you can find someone to do calculations to see what the limits of such a design would be.
And other possibility would be to have a world that gets most of its surface heat from a different source than radiation from its star. Such a world could get much less visible light from its star than Earth gets from the Sun - but enough for photosynthesis to produce an oxygen atmosphere - and get a lot less ultraviolet from the star and so be much more able to retain a dense atmosphere. And it could be warm enough for liquid water using lifeforms in general and for humans in particular. If it had another major source of heat.
And that source could be internal heating of the planet. Internal heating by radioactive decay and by left over heat from the formation of the planet could do a little, but a much bigger source is needed.
And that source could come from the tidal interactions between the world and a companion world. The questions specifies the world is a large moon of a giant planet, so there has to a major companion world to have large tidal interactions with. And strong tidal interactions produce tidal heating.
There has been a lot of speculation about the potential habitability of hypothetical exomoons orbiting hypothetical giant exoplanets in other star systems.
"Exomoon Habitability Constrained by Illumination and Tidal Heating" (2013) by Rene Heller and Roy Barnes, considered many factors affecting the potential habitability of exomoons of giant exoplanets.
https://arxiv.org/ftp/arxiv/papers/1209/1209.5323.pdf
One concept which they introduced in that article was the 'habitable edge" of a giant planet. An otherwise suitable moon orbiting closer to a planet than the "habitable edge" would have too much tidal heating, which would warm up the surface too much and produce a runaway greenhouse effect, turning all liquid water on the surface to water vapor and making the surface too dry for life.
So if your planet and moon orbited far from their star, and received much less than the 1,380 minus 40 watts per square meter from their star that you suggested, they would also receive much less ultraviolet radiation from the star, and even a small moon might be able to retain a dense atmosphere. And if the moon orbited not too far outside the "habitable edge" of the planet, it might have enough tidal heating to warm up the surface enough for liquid water.
Another way to make you world warm enough for liquid water using lifeforms while receiving a low enough amount of ultraviolet to enable it to retain its atmosphere for billions of years, would be to have a lot of greenhouses gases in its atmosphere to make it much warmer than it would otherwise be.
Familiar greenhouse gases are carbon dioxide, water vapor, and methane. And humans can tolerate breathing only slight amounts of them, so if you want to have humans breathing the air on your moon you have a problem. But there are hundreds and thousands of other gases, some of which are greenhouse gases. And possibly there are very strong greenhouse gases which are not toxic to humans. I doubt whether any of the gases listed by Dole would fit the bill, so such gases would probably not naturally be in the atmosphere of your moon.
But possibly an advanced alien civilization terraformed the moon millions of years ago and manufactured those strong, non toxic greenhouse gases and put them the atmosphere of the moon to keep it warm enough for liquid water using life.
So there are three possibilities for a low gravity world to be war enough for liquid water using life while also received low enough levels of ultraviolet radiation for its star that it could keep a dense atmosphere for billions of years.
The density of your low gravity & dense atmosphere world is another factor.
Titan has a mean radius of 2,574.7 kilometers (0.404 Earth) and a mass of 0.0225 Earth. It has a surface gravity of 0.138 g (0.138 Earth) - which is important for how easy it is to fly there - and an escape velocity of 2.641 kilometers per second (0.236 Earth) - which is important for its ability to retain atmosphere for long periods of time.
And note that the surface gravity of Titan is 0.138 that of Earth and the escape velocity is 0.236 that of Earth. The proportion of Titan's surface gravity to that of Earth is not the same as the proportion of Titan's escape velocity to that of Earth. The surface gravity of a world is not proportional to its escape velocity.
And you need a world with as low a surface gravity as possible along with as high an escape velocity as possible to have a world where 10 ton animals can fly.
Titan has a mean density of 1.8798 grams per cubic centimeter, 0.34 of Earth's 5.5134 grams per cubic centimeter. One reason why Titan is less dense than Earth is that less massive world with weaker gravity do not compress matter inside them to a higher density as much as more massive worlds do. Another reason why Titan is less dense than Earth is because it is not make almost entirely of rock like Earth is. Titan is believed to be made about half rock and half ice.
It is believed that the majority of the small worlds in the outer solar system are made of varying mixtures of ice and rock.
If such a world had a surface temperature warm enough for liquid water, it would melt the surface layer of ice many kilometers or miles deep. The world would be covered by a world wide ocean of water much deeper than the oceans on Earth. It wouldn't have any solid land surface. That is a problem except for writers of stories set on water worlds.
That also means that we don't have many examples of low gravity worlds to compare your desired moon with. Most of the small worlds in the solar system are largely compose of ice isntead of being almost all rock.
Io, the innermost Galilean moon of Jupiter, was no doubt originally largely made of ice. But the intense vulcanism caused by tidal heating has probably cause Io lose almost all all its light elements and compounds.
Unlike most moons in the outer Solar System, which are mostly composed of water ice, Io is primarily composed of silicate rock surrounding a molten iron or iron sulfide core. Most of Io's surface is composed of extensive plains with a frosty coating of sulfur and sulfur dioxide.
https://en.wikipedia.org/wiki/Io_(moon)
Io has a density of 3.528 grams per cubic centimeter, a surface gravity of 0.183 Earth's, and an escape velocity of 2.558 kilometers per second. Io's surface gravity is higher than Titan's which is bad, and its escape velocity is also higher than Titan's, which is good.
The Moon has a mean density of 3.344 grams per cubic centimeter, a surface gravity 0.1654 that of Earth, and an escape velocity 2.38 kilometers per second, 0.212 that of Earth. Both values are worse than those of Titan for our purposes.
Ceres has a mean density of 2.1616 grams per cubic centimeter, 0.029 the surface gravity of Earth, and an escape velocity of 0.516 kilometers per second, 0.046 that of Earth. The surface gravity would be great, but the escape velocity would be probably be much too small. But at least the relative escape velocity is higher than the relative surface gravity.
Ceres is not all rock but has a considerable amount of water in it. Thus it might have a world wide ocean covering its entire surface if it was warm enough for liquid water.
Vesta has a mean density of 3.456 grams per cubic centimeter, a surface gravity 0.025 that of Earth, and an escape velocity of 0.36 kilometers per second, 0.032 that of Earth. The escape velocity is even less than that of Ceres. But Vesta seems to be rocky. So it wouldn't be covered with ocean if it was warmer. So a much larger version of Vesta might possibly have a low enough surface gravity and a high enough escape velocity.
