Playing flv files using e.g. mplayer works fine. I'm using pulseaudio, and have an ~/.asoundrc file:
pcm.!default.type pulse ctl.!default.type pulse
alsamixer is working fine and the channels are unmuted.
I moved ~/.macromedia to ~/.xmacromedia as suggested at the end of this post: https://bbs.archlinux.org/viewtopic.php?id=134892.
Didn't even need to restart the browser -- suddenly everything worked.
The question is why is there a ~/.macromedia folder, and what does it do? Might have a look into that at some later point.