It claimed about not being able to detect the cam, whereas VLC finds and uses it perfectly.
Well, there's a known compatibility limitation between the underlying video-for-linux (v4l) layer.
Modern Linux systems use version 2, whereas the Flash applets seem to be comfortable only with version 1.
There's a possibility to force Firefox to use the version 1 of v4l, by launching it this way:
LD_PRELOAD=/usr/lib/libv4l/v4l2convert.so firefox &
Now the Flash applet should be able to detect and use your webcam.
More details can be found in this article I found.
