I admit it. I have a habit of playing "random" characters.
...for example.. my gnome samurai...
anyways;
in a current campaign, my PC died (con dmg poison) and I made a back up at the spur of the moment. I came up with a Female, Raptoran BAR/CLR. Feats include: Pwr Attk, Cleave, Hover, Fly by attk, and Impr. Overrun.
I've read the rules on the Dive technique (included in the raptoran descriptions) and the Overrun manuever (PHB). I (successfully) dived an Orc Bard with a spear, but I would love to charge/dive from the air with my Great Axe. I'm not sure if there are any feats that govern that movement. However, my DM ruled that if I charge (fly) in a straight uninterrupted line, the charge and overrun rules would apply.
How would you handle the situation?
IIRC, you certainly can both Charge and Run while flying.
All the rules for both those situations on the ground apply in the air as well, so you need to have no obstructions blocking your straight line. If there is nothing blocking your way, go for it!