Flash in Ubuntu 10.04 64 bit
Installing Adobe Flash from the repository in Ubuntu 10.04 64 bit gives you the 32 bit version and runs it with nspluginwrapper. I have experienced several problems with this solution in Firefox, and is therefore using Adobes 64 bit Linux version.
Uninstall the repository version of flash
sudo apt-get remove flashplugin-installer nspluginwrapper
Get the Adobes Linux version from http://labs.adobe.com/downloads/flashplayer10_64bit.html and install it:
wget http://download.macromedia.com/pub/labs/flashplayer10/libflashplayer-10.0.45.2.linux-x86_64.so.tar.gz
tar -zxvf libflashplayer-10.0.45.2.linux-x86_64.so.tar.gz
sudo mv libflashplayer.so /usr/lib/mozilla/plugins/
rm libflashplayer-10.0.45.2.linux-x86_64.so.tar.gz
Restart Firefox
Update: June 6th
I have switched back to the "Ubuntu" Flash, because I was unable to use pages from ipapercms.dk:
sudo rm /usr/lib/mozilla/plugins/libflashplayer.so
sudo apt-get install flashplugin-nonfree
The flickering seems to disappear when all the fancy visual effects are disabled.