There are two solutions here that I see, but one is probably more reasonable than the other. Without the use of a streaming media server, you can't really record video/audio. However, the FLV spec is open source and you can accomplish a "recording" by writing bitmap data bytes to a flv file (using the open source spec). This won't capture the audio though, and you can't do that without a streaming server. Also, if you're recording long videos, chances are the writing will either make your application unresponsive/crash it, or the saving time if you broke it down to manageble chuncks would take forever.
The second option, probably what you want, is a streaming server. Whether it be Red5, Wowza, FMS, etc, you'll be able to accomplish what you want, and it should be fairly easy. All be it much more expensive. For what you're describing though, recording live streams, it is probably the most likely approach.