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.
Hideous Laughter can mostly be summarized as "fall prone & skip your turn"
As you noted, the target can take no actions while laughing.
Moving is an action (PFSRD):
The simplest move action is moving your speed.
So is standing up (PFSRD):
Standing up from a prone position requires a move action and...
Taking a 5-foot step ("shifting" in 4e parlance) is an action as well, albeit a weird one (PFSRD):
Miscellaneous Actions
The following actions take a variable amount of time to accomplish or otherwise work differently than other actions.
Take 5-Foot Step
You can move 5 feet in any round when you don’t perform any other kind of movement. Taking this 5-foot step never provokes an attack of opportunity. You can’t take more than one 5-foot step in a round, and you can’t take a 5-foot step in the same round that you move any distance.
You can take a 5-foot step before, during, or after your other [emphasis added] actions in the round.
Attacks of opportunity are not actually actions of any sort (not even immediate actions) as far as I can tell, so the target can take attacks of opportunity by RAW (PFSRD), though this GM would deem that an oversight and disallow AoOs as well.
An attack of opportunity is a single melee attack, and most characters can only make one per round. You don’t have to make an attack of opportunity if you don’t want to. You make your attack of opportunity at your normal attack bonus, even if you’ve already attacked in the round.
An attack of opportunity “interrupts” the normal flow of actions in the round. If an attack of opportunity is provoked, immediately resolve the attack of opportunity, then continue with the next character’s turn (or complete the current turn, if the attack of opportunity was provoked in the midst of a character’s turn).
The part about not being helpless appears to be there to clarify that the target takes no defensive penalties beyond those imposed by being prone (PFSRD):
The character is lying on the ground. A prone attacker has a –4 penalty on melee attack rolls and cannot use a ranged weapon (except for a crossbow). A prone defender gains a +4 bonus to Armor Class against ranged attacks, but takes a –4 penalty to AC against melee attacks.
Best Answer
The creature falls down before becoming prone.
A flying creature cannot be rendered prone. However, the FAQ on flight states:
Since the creature cannot take any actions it thus cannot hover and falls down as per the normal falling damage rules. This means that if they hit the ground after falling 10 or more feet, they take the appropriate falling damage and are rendered prone automatically. If they fall less than that, they are rendered prone from the spell.