Adobe does not make Flash for mobile devices. They tried, and gave up, as it was too power hungry, could not support all the features, and was buggy.
There are some 3rd party iOS web browsers that have a limited Flash emulation in them, but they are not robust. However, what they do have will most likely play Flash videos.
NOTE: Your iMac can run Flash, however, I strongly suppect you are wrong about having Flash on your iPod. I do not know of any iPod music players that included Flash, and as an iPod Touch owner, I know Flash is not avaible for the iPod Touch.
Message was edited by: BobHarris
Adobe has not made a version of Flash for the iPad.
Kappy explains why. https://discussions.apple.com/message/19446567#19446567
5 Flash Player Alternatives http://www.techshout.com/features/2011/01/flash-player-for-ipad-apps/
Top 4 browsers supports flash player on iPad and iPhone
The best ansd easiest way to play Facebook videos is to simply use the Facebook App. It will decode the videos to a usable format and Play them.
As has been said, Flahs can run on an iMac computer just fine, but unless you have one of the flash supporting browsers its unlikely you can play flash in your iPod touch.
Without the use of Third party apps, Flash will never be supported on iDevices like the iPad, iPhone, and iPod Touch.