$ lsof | grep Flash
plugin-co 1038 naner 16w REG 254,2 4442164 7602188 /tmp/FlashXXfHeQqB (deleted)
$ mplayer /proc/1038/fd/16
Oftentimes the output will give you duplicates for the same temporary flash file (FlashXXfHeQqB in this case) with an extra number after the process id, you can ignore all of that. I'm assuming those are child processes. All you need is the process id (1038) and the file descriptor (16). You can safely ingore the character (w) after the file descriptor.Back in the day (Flash 9 or so?) the flash player used to just dump temporary flash video files in /tmp and delete them after you close the browser tab. I guess they figured it was too easy to copy the files out of /tmp so the newer flash player deletes the /tmp file immediately after it creates them. This is why we have to go and grab the open file descriptor.
This will work with most but not all websites. Some websites (Hulu) will use a streaming protocol (rtsp) among other things to make the content harder to get at outside of flash.
This works on Linux, I'm not sure about OSX or BSD.