On Mac OS X, what is the location of the cache in which Flash videos played in Chrome are stored?
Verified with Chrome 10 and Youtube.com
I have a feeling that you are looking to save the cached flash video to edit or whatever you want.
If so, here is my answer: getting it from cache is almost impossible because chrome uses a unique database to store the cache and that is not readable in OS X (or Windows, Linux, etc). There are some tools that can read chrome's database but they don't work for video files (they are created to remove some particular files in the database for debugging purposes instead of saving the files from the database).
So instead of getting it from the cache, you should try to recompile the flash file. This requires extensive knowledge in action script - and a smart hacker's mind (some developers are very good at confusing hackers so you get the wrong idea). I can't cover it. Finally if you do get the video file's url, make sure you have the right tool to download it. You will need to fake your origin (browser, cookie, etc) most likely.
Alternatively, you can do a screen recording to get the video but the quality will not match from source file.
Lastly if you were looking for a video you watched but forgot where it is on the web (or removed), you are completely out of luck. There is no way to get it out. You have to find some senior engineer at Google who knows exactly how chrome read its database to help you (and likely such knowledge is a collaboration of a few engineers, so you must get the whole team on board). In this case it is actually as hard as hacking into DMV database to change your driving records.
Hope this helps.