Not sure if this will help, but it seems to me that when you get this material, it resides in a cache on your computer. I've had good luck using Opera's cache to get hold of elusive data, though I don't recall ever getting anything from Flash that way. Once you have some sort of file, you can no doubt figure out a script to snag the data.

If you try this approach, I highly recommend emptying your cache just before accessing the pages you want, to eliminate the often massive amount of old stuff you don't care about.