Not sure if my experience will help or not. I'm running 2011.1 64bit
The first time I tried to run a flash movie in Firefox it wouldn't run. It said I needed a plugin update.
I had the latest stable plugin but found that there is an 11.0 beta plugin available but it's in a tar.gz package and I didn't install it. Here:http://labs.adobe.com/downloads/flashplayer11.html
I rebooted Firefox and it started to play my flash movies fine.
After reading your post I tried Konqueror and it did the same thing, wouldn't play, said I needed an update.
I went to Settings/Configure Konqueror/Plugins/the Plugins tab/Scan for plugins button. It ran a scan, I clicked on the flash movie once more and it played just fine. Guess it just had to locate the updated plugin.
Strange, I know. Just thought I'd share.
Wish you the best.