Is there any way to mute other flash objects on the same page with ActionScript or Javascript? I can understand if this would be a security issue but my flash does have a user-initiated mode which takes over the screen and I was hoping this might be an exception where it's clear it has full priority for the user.
Exposing internal controls in a Flash movie is up to the programmer who writes it. If they haven't exposed an external mute/volume control and have documented it, you're out of luck. There is no universal API that can be called.