In Replay Media Catcher go to "Fix FLV", Expand the "File contents". Use the framerate shown on the web-site. Hit the "Fix Time" button.

After this fix, the segment plays fine for me in Applian FLV Player and KMPlayer. But I have problems playing with VLC player and Media Player Classic with K-Lite Mega Codec Pack; may be I just used wrong framerate value.

Also please note there could be lots of problems downloading/capturing RTMP streams. And since you plan to convert your recordings anyway, it can be much better to record from screen instead of downloading/capturing.