Quite awhile ago Flash started "deleting" the file in /tmp as soon as it got the file handle. You can still get the file handle using 'lsof' while the video is playing. It would be easier to just use a tool like youtube-dl or clive (or a browser extension) to grab the videos, though.

Not anymore, a Flash upgrade broke that sometime ago.

I use the following script on Arch to do what you're looking to do: http://pastebin.com/9si8EdFQ