unfortunately true streaming doesn't save the file to local disk and plays directly from the server.. this is much more common with audio files than video due to copyright issues and mainly bandwidth since true streaming will require much more bandwidth because every time the user pauses, skips or replays a file it ill have to be streamed from the server where as just saving a tmp file means the file can be reused as long as it's cached. naturally websites try to avoid that with video files which are much bigger and reduce costs. some audio websites do not adapt true streaming but those are rare and becoming less as record companies pressure them into streaming.
was one of those few no-streaming music websites but it got bought by myspace recently and now they use true streams
fla video server can't save audio streams because there was never a copy on disk to start with. the best way to save those audio streams is with a good sound recorder which can record directly from the sound card.
one of the best sound recorders is audacity which is available for many platforms:
another program called liveincode doesn't have special filters or advanced editing features which makes it perfect for that task
it's for windows only