Where are FLV cache files stored?
This may vary by browser, but in Safari, if you press ⌘⌥A, you bring up the Activity window. Find the largest file being downloaded for the current page; that is generally the Flash Video. Double click it, and it will be downloaded to your downloads folder.

This avoids having to learn the various places Mac OS X will store temporary files on disk. In general, things that aren't expected to be cached for re-use end up in /private/var/tmp and things that are in ~/Library/Caches but in your case, safari will expose that file more directly and allow you to fetch it.

If you are ever curious - you can watch filesystem activity in real time with some quick commands like sudo fs_usage -w | grep Safari