Hm.... now it only works sometimes. If I restart my computer and go right to something like Youtube, the videos will play with sound. If I start to open other programs, like Songbird and Pidgin and then try to play more videos later, they'll play without sound.
If I install the libflashsupport package, is there anything else I have to do or is it just install the package and leave things alone?
Edit:
Additionally, I just found if I close off Songbird (altogether) and restart firefox, flash videos work again. Maybe Songbird is taking over the sound driver (even when it is stopped) and prevents other stuff from playing sounds?