When you download .flv files with flash they are in your /tmp/ folder (or whatever your crazy OS uses for temp data). Most flash players are "vulnerable" to this.
Most flash music players will first send an HTTP request saying "Hey, I want this file can I have a token?" This token is then used to authorize the music download. This makes it so you can't have some easy to forge get/post request to download the file, you actually have to simulate a protocol interaction which most children can't do. Most public "hacks" don't even use a browser, they just simulate the behavior of a browser and ignore any "security though obscurity" measures you put in place. Most children love these downloaders.
Although it is trivial to decompile most flash applications an attacker is going to look at network traffic because its a lot easier. Tamperdata defeats a system of "transactions". In fact I have never seen a protection system like this that can't be defeated with Tamperdata. You let the Flash player make the request for the token, then the next request for a mp3/flv file can be intercepted and then dropped. You can then replay this request and download the file normally.
This is a "client side trust" issue and THERE WILL NEVER BE A SOLUTION. But it looks like you know that and you are looking for security though obscurity.