The binaries available here are freely redistributable (cover mount CD/DVD, download site,...) BUT they must be redistributed as they are. In particular, it means you cannot alter/replace the installer to bundle avidemux with other programs (for example: browser toolbars). Doing so would invalidate your license to redistribute and you would be providing counterfeiting software.
I did another test and the result is way better now. Still the speed is not the same as in avidemux but now is way faster. The quality, it seems, is the same as before, so, the quality, for me and my needs is good enough.
Newer versions of Flash support H.264 as a video codec but it's a relatively new development so I encountered trouble getting avidemux to encode H.264 stream into an FLV file directly. The workaround I used was to save the video in a different container format and then use a relatively new version of FFmpeg to repackage the video into FLV:
35fe9a5643