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.
Best Answer
Yes
You've quoted the relevant rule, and standing up would count as a move action that doesn't move the character out of the square.
So Standing would trigger the reaction, but the trigger would happen after completing the Stand when the character is likely no longer prone. On a failed save against Impede, the character would go back to being prone.