Is it possible to have too small a navel flap to get it pierced successfully?

It is possible, but actually rare. Even people that dont have a very defined navel "lip" can still get a navel piercing; it is what you call getting a shallow piercing, meaning there is not much skin to pierce through. I have seen successful healing with shallow piercings, and I have also seen some that are not so successful. Talk to your piercer about whether or not it is a good idea for you to get one.