You can download RTMP streams with freeware StreamTransport, CooJah + Blader, shareware Replay Media Catcher,...

And you can capture RTMP streams in real time while you watch them using freeware CooJah (without Blader), Orbit Grab Pro, shareware Replay Media Catcher 4.

Replay Media Catcher can convert downloaded video to iPod compatible formats: m4a or m4b audio, mp4 (m4v) video. You can also use other audio/video converters like freeware Videora iPod Converter.

Related:
FAQ: How to record/download/capture/save Adobe Flash .FLV video RTMP stream from embedded player
How to record rtmp:// flash video .flv stream from embedded Adobe Flash Player