Well, I'm using ffmpeg all the time. It is very good.
Saving a stream is actually very easy. You can tee the stream to disk while it is playing, you can use tcpdump to send the packets to disk, you can use ffmpeg to read the stream and send it to disk, you can use ffmpeg to send the whole screen to disk you can use mplayer to save the stream to disk, you can use streamtuner, or you can play the video with Firefox and then go and troll through the tmp directories to find it - Firefox dumps it somewhere while playing...
Of all the methods, using VLC is prolly the worst, since VLC is very buggy. Using kdenlive to record is simply wrong headed and using mplayer is one of the easiest:
-dumpstream -dumpfile outFileName
and you can do it all at the same time:
You can also do the same with ffmpeg and ffplay.
However, recording a stream assumes that you know what you are playing, e.g. mp4. If you use ffmpeg and the output file is .mp4 while stream is something else, then it will transcode the stream, which is probably not a good idea, since it is very processing intensive.
Therefore, getting it to work is NOT easy, since there are so many variables and unknowns that you have to investigate.