There are programs that will do a soft-waveout mix... like WinADR for example. I used this to record the audio for a flash file I was converting to DVD.
Failing this, go into Volume Control > Options > Properties > Recording.
IF there's a "Wave Out" or something to that effect, check that box, and any sound recording program will record every sound the computer makes. Turn down your speakers or just turn off your microphone to avoid feedback and you're set.
If there isn't any such option - perhaps installing generic sound blaster drivers will provide one?
ALSO: if you can get your hands on the actual SWF files (raid your temporary internet files, or view source on webpages and use a client like GetRight or something to download them) .... then you could try various Flash extraction programs, that let you get at the assets.