This scenario would not work as described.
In D&D 5e, falling is treated by default as resolving instantaneously, though Xanathar's Guide to Everything has an additional optional rule for the rate of falling (p. 77):
The rule for falling assumes that a creature immediately drops the entire distance when it falls. [...] If you’d like high-altitude falls to be properly time-consuming, use the following optional rule.
When you fall from a great height, you instantly descend up to 500 feet. If you’re still falling on your next turn, you descend up to 500 feet at the end of that turn. This process continues until the fall ends, either because you hit the ground or the fall is otherwise halted.
Note that the rule only addresses falls of over 500 feet (yours is only 300 feet). Given that fact, the fall itself would be immediate once it started, so if you're readying an action, you'd have to do it before the fall - it'd have to be a planned fall.
In addition, note the mechanics for the Ready action:
First, you decide what perceivable circumstance will trigger your reaction. Then, you choose the action you will take in response to that trigger, or you choose to move up to your speed in response to it. Examples include "If the cultist steps on the trapdoor, I'll pull the lever that opens it," and "If the goblin steps next to me, I move away."
When the trigger occurs, you can either take your reaction right after the trigger finishes or ignore the trigger. Remember that you can take only one reaction per round.
When you ready a spell, you cast it as normal but hold its energy, which you release with your reaction when the trigger occurs. To be readied, a spell must have a casting time of 1 action, and holding onto the spell's magic requires concentration. If your concentration is broken, the spell dissipates without taking effect. For example, if you are concentrating on the web spell and ready magic missile, your web spell ends, and if you take damage before you release magic missile with your reaction, your concentration might be broken.
Even if you were able to choose a perceivable circumstance that occurs before you hit the ground (remember that the readied action takes place after its trigger), the problem is that when you ready a spell, you cast it immediately - when you take the Ready action - but hold its energy.
The Storm Sorcerer's Tempestuous Magic feature (Xanathar's Guide to Everything, p. 51) states:
Starting at 1st level, you can use a bonus action on your turn to cause whirling gusts of elemental air to briefly surround you, immediately before or after you cast a spell of 1st level or higher. Doing so allows you to fly up to 10 feet without provoking opportunity attacks.
The issue with your proposed scenario is that by the time you're falling, you've already cast the spell - so as soon as you take the Ready action, Tempestuous Magic triggers.
If you ready a spell before you fall, it's too late to try and fly as you're falling - and unless you fall exactly 501-510 feet, you don't have a chance to take an action to cast the spell right before you hit the ground.