Firefox for Geeks and Power Users
a. Type about:blank in the Firefox address bar
b. Now click List cache entries or directly type about:cache?device=disk (Disk cache device)
c. Press Ctrl+F and try to location the flash file by typing some part of website URL or the flash file name or just .swf. After some hit and trial, you should be able to locate the swf file URL
d. Click the SWF URL to open the Cache Entry Information page. Right click on the link and choose "Save link as"

I use "about:cache?device=disk" a lot, one tip though is clear your private data before loading the page that has the file you want, you'll have way less things to sort through to find it. With videos its usually pretty easy to find cause it'll be a really big filesize compared to all the other entries.
As well you need to let the video play/load fully before it'll show up.
This works for many types of files flv, jpgs, etc and saves you from having to install extensions/add-ons.