If a flying creature takes falling damage from the fall due to being knocked prone, it is prone on the ground, otherwise it lands safely.
Prone:
When a creature is prone, it is lying down. If the creature is climbing or flying when it is knocked prone, it falls instead.
Therefore, flying creatures fall.
Flying:
Falling Prone: If a creature falls prone while it is flying, it falls. This means a flying creature falls when it becomes unconscious or suffers any other effect that knocks it prone. The creature isn’t actually prone until it lands and takes falling damage.
Therefore, a flying creature may or may not be prone, depending if it takes damage.
Crashing:
Falling while Flying: If a creature falls while it is flying, it descends the full distance of the fall but is likely to take less damage than a creature that can’t fly. Subtract the creature’s fly speed (in feet) from the distance of the fall, then figure out falling damage. If the difference is 0 or less, the creature lands without taking damage from the fall. For example, if a red dragon falls when it is 40 feet in the air, subtract its fly speed of 8 (8 squares = 40 feet) from its altitude. The difference is 0, so the dragon lands safely and is not prone.
If a creature is flying when it starts a high-altitude fall, it has one chance to halt the fall by making a DC 30 Athletics check as an immediate reaction, with a bonus to the check equal to the creature’s fly speed. On a success, the creature falls 100 feet and then stops falling. On a failure, the creature falls as normal.
Therefore, if a flying creature is knocked prone at a distance of more than its fly speed, it takes damage and is knocked prone at the end of its fall. If a flying creature is knocked prone at a distance of less than its fly speed, it is merely grounded until it can take off again (provoking attacks of opportunity as appropriate.)
As a curious note, inflicting the "slowed" condition on a flying creature before knocking them prone is an excellent way of causing them both falling damage and being prone at the end of the fall, as the slowed condition reduces their speed.
The only movement allowed a prone creature is crawling, teleportation, or forced movement:
A prone creature takes a -2 penalty to attack rolls, and the only way it can move is by crawling, teleporting, or being pulled, pushed, or slid.
Therefore, a prone creature cannot fly.
Hover may prevent a creature from falling prone, but only from inference
Fly Speed:
A creature that has a fly speed can fly a number of squares up to that speed as a move action. If the creature is stunned or knocked prone while flying, it falls. See also hover.
Hover:
If a creature can hover, it can remain in the air if it is stunned. See also fly speed.
There is an argument to be made that knocked prone is countered by hover due to hover also countering stunned. It is not present in the rules however.
A creature hovering or flying one square off the ground with a fly speed of more than 1 lands safely when knocked prone, and therefore does not take falling damage. The lack of falling damage means that the creature is then not prone.
A creature flying at ground level is still in the "flying" mode of operation. and there are no minimum altitude rules. It can be assumed that a creature with hover will be flying at all times, and a creature with flight but without hover will be flying whenever there is little chance of being stunned or when its fly speed is greater than its ground speed.
In this section, it says
This rule is helpful to a flier that is knocked prone but is still conscious and has a current flying speed that is greater than 0 feet. The rule is designed to simulate the creature flapping its wings furiously or taking similar measures to slow the velocity of its fall.
Meanwhile, the rules for flying say:
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.
... so, there are different ways to knock a flying creature out of the air. Note that the prone condition doesn't reduce your speed — and it's clear that that's the case that the new optional rule really applies to. In that situation, the creature can't fly and falls, but can flap or take whatever measures. The rule notes that if the fall continues for more than one turn (that is, more than 500 feet), a "prone" creature with a fly speed can recover. Other more powerful means which reduce the target's flying speed to 0 still mean a dangerous fall.
But, also note that Earthbind is not one of these more dangerous situations, since it explicitly gives a soft landing:
An airborne creature affected by this spell safely descends at 60 feet per round until it reaches the ground or the spell ends.
(The text does not specify "no damage", but it's implied by "safely" — and note that this is the same rate that Feather Fall provides.)
So, to directly answer your question: being prone has no effect on the calculation. As the optional rule says, subtract the creature's flying speed from the distance fallen and then calculate damage as normal (1d6 bludgeoning damage per 10 feet) for the remaining distance.
Best Answer
From the Player's Basic Rules (v0.2), page 71:
So a flying creature that is knocked prone will fall, unless it has the ability to hover, in which case it will remain where it is. In the specific case of the elemental, it is immune to the prone condition, so nothing will happen to it. But even if it wasn't, it has the ability to hover, so it wouldn't fall anyway. (Or, as SevenSidedDie puts it, double-nothing happens.)
Note that whether it can hover or not, unless the creature is immune to the prone condition the other effects of the prone condition apply. So the creature's attacks have disadvantage, and attacks against the creature have advantage if they are made from within 5 feet, or disadvantage if they are made from further away.