Well, it's a mix of your own magic and the brooms' magic. They use enchanted wood, and then you have to meet it halfway in order to will yourself to fly... I'm still working on this part myself, to be honest. I know how it works, but.

[ He's... he's not good at flying. It's Azul's Achilles heel. Fish don't fly- he only gets like two feet off the ground normally. ]

The flying portion still eludes me.