Man, lots of haters in this thread.
Y'know what? This is 4e. Reskinning is the name of the game. It sounds like the Pixie coming up might be what you're looking for in an ideal world, but lets go with what there is now.
There's two races that have bog-standard flight right out of the gate: Airsoul Genasi and Githyanki. I'm guessing the Airsoul Genasi would be a better match for his idea (Githyanki flight is less far, but it can be done to an ally as well).
If "fly every once in a while" doesn't grab your player, then giving some other race an Overland Flight speed is fairly harmless, as well. It's limiting factor is that you (basically) can't do anything else with it but fly. You could slap this on any race without too much harm, perhaps removing the usual racial power for it. To be a hawk, I might suggest going small -- gnome or halfling.
Those are the Easy Ways.
The Hard Ways generally involve inventing your own flight mechanics. Rules like: "If you take damage, you must land at the beginning of your next turn," or "You can't attack while flying" come in handy, though the later is blatantly gamist, and the former might mean he still rocks in any combat with melee machines...though at that point, almost ANY ranged class keeps their distance, hawk or not.
Flight is workable.