If you have installed the Ubuntu Restricted package you must first remove the 32-bit Flash plugin before attempting to install the native 64-bit Adobe Flash plugin.
To remove the 32-bit Flash plugin open a terminal and type the following,
sudo apt-get remove flashplugin-installer nspluginwrapper
How to install the 64-bit Adobe Flash Plugin
First, download the 64-bit Flash plugin from Adobe.
http://labs.adobe.com/downloads/flashplayer10_64bit.html
By default Firefox in Ubuntu 10.04 will download all files to the Downloads folder in your home area.
Next open a terminal and type the following,
tar -xf ~/Downloads/libflashplayer-10.0.45.2.linux-x86_64.so.tar.gz
sudo mv libflashplayer.so /usr/lib/mozilla/plugins
The 64-bit Flash plugin is now installed.
Enjoy.
