That's up to the person that writes the Flash audio player. By itself, Flash Player will not display any user interface.
Buy why can you see the elapsed time in Internet Explorer on Windows XP, and not in Safari on Mac OSX?
I'm not sure, what web page are you listening to audio at?
Screen shot in Windows 7 / Internet Explorer 9.0 / Flash Player 18.104.22.168:
Screen shot in Mac OSX 10.6.8 / Safari 5.1.7 / Flash Player 11.3.300.257: