Let's put this in terms the OP can understand.
For this example, I'm gonna assume you use Metallica's music for your flash.
You make a flash, you use Metallica's music in said flash, your flash makes money, Metallica sues you. Why? Because you are making money off of something you did not in fact make. Doesn't matter if it's a small little 10 second "Oops I did it again" clip with a stick man knocking over a vase... If you profit off it using Metallica's music, without making prior agreement with them, you go to court.
The same is true of musicians on the AP. Get their consent, work out a deal. If you just make a flash and slap someone's music on it without their consent, and you make money off of it, that musician has the right to take legal action against you.
Using someone elses work and making money off of it is stealing, no matter how famous they are, no matter how small your project. If you're going to use someones music, work out some kind of deal. The worst that could happen is they say no, and you look for another musician. If you don't work out a deal and just use it behind their back, the worst that could happen is you go to court for theft.