Given that it is possible to jump as part of a charge (remember Leap Attack?), you CAN charge normally by taking a full-round action and leaping off a ledge.
Actually, Rules Compendium specifies what kind of jump can you make as a part of a charge (hint: it's long jump). FAQ clarifies that e.g. high jump is not possible because you change direction (unless you take a feat like Fleet of Foot or Psionic Charge that allows you to change direction). Similarly, when jumping off a ledge, you first move 5 ft ahead and then move/fall/jump down, so that's a 90 degrees turn, i.e., no charge. Also, you're going around a corner, i.e., no charge.
Battle Jump is another feat that allows these unorthodox jumps while charging, and, it also grants you various other benefits, e.g. double damage. Good enough for a feat.
I would tend to agree with this - with the exception of giving the RC too much weight. But ok, it's a clarification.
I'm not entirely sure that it's strict RAW, but the I believe letting falling count as movement while you are doing it intentionally should be in order. I think the rules tend to make that distinction - intentional falling, such as when you are dropping after a high jump, counts as moving. But when you fall unintentionally, i.e. from stalling with poor maneuverability, or from falling into a trap, then it doesn't count. I believe the rules are also inconsistent on this: Gliding with wings, for instance, does not count as movement. Also, other types of movement which do no take YOUR actions still preclude full-attacks - such as when using a mount.
IMHO the game should have been designed with more consistency in that respect: Either movement ALWAYS counts as your move action - and then falling might give you a "falling"-bonus to movement speed, or it consistently does not count when you are not actively doing anything - such as when are falling, riding, gliding, etc.
After those deliberations, what I also believe does not work is dropping only five feet towards an opponent with a reach weapon, you do have to move 10 feet, even with Battle Jump.
So the OPs action sequence is this:
Fly over an opponent, with enough room to drop 10 feet on top of him to hit him.
Drop intentionally by folding your wings, drop 10 feet, this counts as a charge, you hit or pounce him. You also gain 5ft of movement. Either falling counts as movement or it doesn't.
Now either this counts as a FRA, in which case your round is now over, or it doesn't. In which case (like with Sudden Leap multipouncer models), you can still move.
You fly up again 10 ft vertically, and drop again. Rinse repeat.
What I suggest concerning movement:
Falling itself should be a non-action, or a free action that simply happens when it happens. Falling in a controlled manner, now that should, IMHO, count as movement. If you are falling in a way so that you can stop yourself at any time, then it's not the same as simply dropping. There is also a difference in speed: Uncontrollably dropping makes you fall 150 feet in one round (and 350 in the second). The fastest speed you can fly vertically down at is twice your normal speed - even for perfect maneuverability. (Now with fast fly speeds this can be faster than just dropping... which is just another one of those weird things.)
So, I propose letting the dropping count as movement, and letting the charge not be a FRA. But that's just me...
(I have to say, though, "execute a charge" does give a strong argument to the full-round-action thing.)