Linux Flash Player with 2 Monitors: always full-screen on primary monitor
Old question but this was the first result I got when searching for the same issue, so if anyone finds this, here's a workaround.
A lot of sites that show flash videos allow you got the video in a "popup", this is usually a special window that only contains a flash player that automatically scales to the size of the window.
Use the popup on the screen you want it maximized on and then use the fullscreen mode of the browser (F11 in Firefox and Chrome). This will use the regular flash container, but scaled to fill your screen.
Edit: If the site doesn't give you the option to use a popout, this addon for Firefox is useful: https://addons.mozilla.org/en-US/firefox/addon/flash-game-maximizer/
One option would be to use a tool like http://www.downloadhelper.net/ to get the video file from the flash object, then use a real movie player to display it properly - you will get better quality, smoother playback, and a real movie player is more likely to figure out how to display on the monitor you want.
A more hackish way is that you can actually navigate to /tmp/ and the flash video file will have a name like FlashxyZAbc, you can directly open that file with a movie player and play it (I have my file manager set up to launch my favorite movie player if I click on one of these files), without needing to install any addons or plugins.
Edit:
concerning the objections posted, mplayer and vlc can download or play rtsp streams, and the flash files in /tmp or the downloads from a downloader addon are playable as soon as the first few frames are downloaded.
You mean this ? : http://my.opera.com/d.i.z./blog/2009/04/22/watch-fullscreen-flash-while-working-on-another-screen
Guess this is what you want.. but I'm not sure, worth a 'try-answer' :)