One workaround would be to install 32-bit Firefox from Mozillla repository and install the 32-bit Adobe fFash player plugin. The other way would be to install the beta version of the 64-bit Adobe Flash player which is now available from other repositories. Following are the steps:
1. Remove all other flash plugin intallations. Use the following shell script
#!/bin/bash
apt-get remove --purge flashplugin-installer
apt-get remove --purge flashplugin-nonfree gnash gnash-common mozilla-plugin-gnash
apt-get remove --purge iceweasel-flashplugin mozilla-flashplugin firefox-flashplugin
apt-get remove --purge swfdec-mozilla libflashsupport nspluginwrapper iceape-flashplugin
apt-get remove --purge xulrunner-flashplugin midbrowser-flashplugin xulrunner-addons-flashplugin
rm -f ~/.mozilla/plugins/*flash*
rm -f /usr/lib/firefox-addons/plugins/*flash*
rm -f /usr/lib/firefox/plugins/*flash*
rm -f /usr/lib/iceape/plugins/flashplugin-alternative.so
rm -f /usr/lib/iceweasel/plugins/flashplugin-alternative.so
rm -f /usr/lib/iceweasel/plugins/npwrapper.libflashplayer.so
rm -f /usr/lib/midbrowser/plugins/flashplugin-alternative.so
rm -f /usr/lib/mozilla/plugins/*flash*
rm -f /usr/lib/xulrunner-addons/plugins/flashplugin-alternative.so
rm -f /usr/lib/xulrunner/plugins/flashplugin-alternative.so
rm -f /var/lib/flashplugin-nonfree/npwrapper.libflashplayer.so
Save the above script in a file say... remove_flash.sh and give it executable permission
$chmod u+x remove_flash.sh
Download
2. Add the following to the Software Sources:
http://ppa.launchpad.net/sevenmachines/flash/ubuntu lucid main
One way to do this is through Applications > Settings > Software Sources.
Once added issue the following command:
$ sudo apt-get update && sudo apt-get install flashplugin64-installer
Check opening firefox and opening up any youtube video.