You descend 60 feet per round unless you end the fly spell
I refer to the same passage that has been quoted in the other answers (PHB p. 191):
If a flying creature is knocked prone, has its speed reduced to 0, or is otherwise deprived of the ability to move, the creature falls, unless it has the ability to hover or it is being held aloft by magic, such as by the fly spell.
(Emphasis added). This means, while under the fly spell you will not be able to fall, also not when "dropping prone".
If you cast the fly spell upon yourself (or the caster cooperates), you or they could end concentration on the spell, causing the spell to end. At that point, unless you have a natural fly speed, you will be falling.
On p. 183 PHB:
A fall from a great height is one of the most common hazards facing an adventurer. At the end of a fall, a creature takes 1d6 bludgeoning damage for every 10 feet it fell, to a maximum of 20d6. The creature lands prone, unless it avoids taking damage from the fall.
There are no specifics about the fall in the core rules. Your DM either can rule it is immediate, or based on the assumption that everyday things behave as we would expect them to, they could also rule that there is a maxium drop rate due to air resistance and such per round. Variant rules in XGE (p.77) offer 500 feet per round:
When you fall from a great height, you instantly descend up to 500 feet. If you're still falling o non your next turn, you d escenddescend up to 500 feet at the end o fof that turn. This process continues until the fall ends, either because you hit the ground or the fall is otherwise halted
If you are using such a rule, you could try and take other actions to regain the ability to fly before hitting the ground. Depending on the height you may have leisure to do so.
If the height is less than what you would drop in one round: ending concentration is not an action, so you likely could take a triggered action for the round where you fall to re-cast Fly shortly before hitting the ground&. This of course would cost you another spell slot use.
If you are interested, this answer provides an excellent summary of the mechanics and timing of falling.
& Thanks to Thomas Markov for finding this.