OK we have mixed devices here so let's see if I can head off any confusion at the pass ...
My comment quoted above refers to the original RedFly that has no dedicated video playback support. If you have the newer RedFly that supports Video out from your device, then video, and I mean AVI whatever, will work as advertised.
So far as I understand it - I've not tested so I cannot state definitively - Flash video is not supported under this scenario unless your device specifically supports exporting Flash video to an external screen via TV out. Perhaps your device will display anything that could be displayed on the device screen, in which case Flash video will play fine.
If your device has no dedicated video out, then you are left with whatever the RedFly and a USB cable can cope with. If you have simpe Flash content - let's assume text and images, limited animation, no fancy alpha blending, tweening etc, then it should play fine through the RedFly. My own tests with the new Adobe Distributable Player, and some sample content created with Captivate 4 (I was beta testing both
http://stevehoward.blogspot.com/ http://stevehoward.blogspot.com/2008/11/adobe-shows-off-captivate-4-and-adobe.html) show that simple content will work fine with RedFly, but as with all content, the screen refresh rate is probably about 4 frames per second max, so don't expect stellar visuals. If you know your content is simple, it will work with the RedFly since the actual limitation is ... do you have the Flash player installed.
Hope this clarifies, but feel free to ask for more info.