Clever web developer Rafael describes how he used the Live HTTP Headers Firefox extension to download the MP3 behind a Flash player:
What the liveHTTPHeaders extension does is show you the browser's http requests. I use it a lot in web development work to make sure that Flash is requesting data correctly. This tip will always be handy when you come across a site that obscures media through flash.
Rafael used Live HTTP Headers to grab the MP3 from a Flash player playing the theme from Californication, but in theory this will work for other players (a cursory test on YouTube and MySpace didn't turn out much, though).