I'm looking for a way to make MP3's from audio that's mixed in a Flash UI audio
mixer. It'd have to be done server-side and was wondering if there was an
application that could interface with Flash on a server and spit out mp3's to
a user that has mixed the audio on a Flash mixer.

Is there anyone with suggestions or information on the subject?

You can do that with FMS, but since you can't use a sound object as a mic
(wouldn't that be neat?), we need to record from wav sound instead of mic audio.

What your users will need to do is open their sound mixer, select the
recording properties, and enable recording of wav sound or the stereo mix. Now
you'll be able to publish the mix to FMS and record your audio... which will be
in flv format, and in mono. You'll need to use a third party program to extract
the audio from the .flv and create the mp3 file.