How was Eärendil's ship Vingilot able to fly?

Question

Eärendil's ship Vingilot was built to sail to Valinor so that Eärendil could make his plea for the Valar to help Men and Elves under Morgoth's reign over Middle-earth. After the Valar agreed to help the peoples of Middle-earth, Manwë sent the Host of Valinor to fight Morgoth and his armies of Angband.

It is said that Eärendil with the Silmaril aboard his now-flying ship, along with Thorondor and his Eagles, defeated Ancalagon the Black.

Now what I want to know is: how was Eärendil's ship able to fly, and who made it a flying vessel?

Answer 1

"Flying" was not an unique trait to Vingilot. After the fall of Númenor the Valar reshaped the world, so that only elven ships following the "straight road" could reach the undying lands. (This happened long after the voyage of Eärendil):

The ‘immortals’ who were permitted to leave Middle-earth and seek Aman — the undying lands of Valinor and Eressëa, an island assigned to the Eldar — set sail in ships specially made and hallowed for this voyage, and steered due West towards the ancient site of these lands. They only set out after sundown; but if any keen-eyed observer from that shore had watched one of these ships he might have seen that it never became hull-down but dwindled only by distance until it vanished in the twilight: it followed the straight road to the true West and not the bent road of the earth’s surface.

Tolkien's letter no. 325 (emphasis mine)

It is my understanding that the ships do not really fly, free to choose their altitude; rather that there are certain passageways in Tolkien's universe that are intangible and invisible, but can be navigated by a ship, when it has been hallowed. That does not necessarily mean the ship is in any form physically altered, merely that the Valar permit it to use that road. (Although the quote does talk about specially made ships, so perhaps some alteration is required.)

The straight road was one such passageway that many elven ships could use. The "oceans of heaven" were another passageway, and the only ship reported to sail it was the Vingilot, but that does not mean it was altered to become a flying vessel, different from the other elven ships sailing the straight road.

Answer 2

But they took Vingilot, and hallowed it, and bore it away through Valinor to the uttermost rim of the world; and there it passed through the Door of Night and was lifted up even into the oceans of heaven.

^{The Silmarillion | OF THE VOYAGE OF EÄRENDIL AND THE WAR OF WRATH}

This passage explained it. The Valar hallowed the boat, which means to make it holy. They obviously imbued it with the power to sail the skies.

Answer 3

Simple. Manwë wanted to reward the son of Tuor, but could not allow him to return to Arda because he broke the rules by stepping on Valinor. I believe it was Mandos that wanted to punish them for this, but Tulkas and Aulë intervened and convinced Manwë, the king of the Ainur, to have pity on the blood of the Noldor.

So, Manwë, who would not allow Eärendil to stay in the undying lands, for he was man, and the gift of Eru to men is death. Manwë could not disobey god so he blessed Eärendil's ship, Vingilot, to sail the heavens (the skies) and watch over Middle-earth with the Silmaril, which Galadriel refers to when giving Frodo the light vial. And sometimes, Elwing was given the form of a bird so she could be with her husband for a time.

So when the war came in which Melkor was finally defeated, Eärendil from the skies saw the Black Dragon, he attacked from above with the power of the Silmaril.