Sorry jderosa3, I don't have any experience with the streaming media server. If the flv's work locally then my guess is your exports from Final Cut are okay.
Are you using absolute pointers to your flv's?
Here is a link to an Adobe Labs flv checker. This might help you identify any issues that might be present in your exported flv's.
Also, here is another link to a
Flash Developer Center with some info you can cross reference.
If you're still stuck, I would suggest a visit to the
Video section of
Flashkit and see if someone (with more experience can help determine the problem)
Good luck!