You won't have much luck with that, I tried to view some online flash video in a virtual machine (we all know how fucked flash is on Linux), which lost the audio/movie sync after about 20 minutes.
It being in a virtual machine doesn't necessarily have anything to do with the problems; Audio/video sync in lots of flash content doesn't even work properly outside of virtual machines.
I'd put the odds over 80% that it's just because the VM wasn't fast enough. You then have two options. One is to get a faster machine, the other is to run the VM in slow motion while you save. Obviously the second isn't an option for realtime viewing.