Flash can not only play videos, it can also easily go full screen (without the chrome) to run them with hardware acceleration.
We have a project where we display student portfolio videos, and the client has asked to add a full screen provision. I was looking around the net for this, and found some good resources.
So if you want to add a full screen provision to your Flash Video player too, go ahead and check these out:
Adobe’s Developer Network article explains going to Full Screen mode in Flash Player 9 in detail. It covers both Flash and Flex.
Flash FLV player with Full Screen, source code included. Site in German.
FlashCom Guru has some examples. More than the full screen feature, I loved the BBC clip he used for the demo!
The task looks much easier now! Just need to work a bit on the skinning of the player!