There are two ways you can do this: 1) Completely empty your browser cache, then reload and watch the flash video. Now check for the files in the cache directory* for your particular browser. All the files should be there.
2) Using Firefox, install the 'Firebug' extension. With the extension open, enable the 'Net' tab. This will show you all files being fetched in real time (refresh any page to see it in action).
*You'll have to Google for the location of your browser cache directory because it depends on your operating system, browser and sometimes weather or not you are using multiple logins or a single shared login.
** If the flash player "calls home" for a reason other than fetching more content you might be out of luck. For example, it might query the server intermittently for the specific purpose of make sure it isn't played offline.
Good luck.
