The first thing I'd check are your publish settings.
It could be that you need to set your .fla up to use the network rather than the local filesystem. This is part of the security sandboxing for flash.
I think by default it is set to 'use local filesystem', which is probably why it works locally for you, but does not work on the server. Perhaps try changing that setting to 'use network' instead and then re-export your .swf uploading it to your server and testing it.
It's been a considerable while since I used the flash IDE, so I can't remember exactly where you need to go to get to the publish settings...I think it might be something like 'file->publish settings' from the menu, but I could be wrong!
Anyway, that would certainly be my first port of call, so give that a shot and let me know how you get on.
Cheers for now,
Jas.