Download the 10.1 tar.gz package from Adobe:
wget
http://download.macromedia.com/pub/l..._092710.tar.gz
Then extract the package.
INSTALL:
sudo mv libflashplayer.so /usr/lib/mozilla/plugins/
sudo nspluginwrapper -i /usr/lib/mozilla/plugins/libflashplayer.so
sudo ln -sf /usr/lib/nspluginwrapper/plugins/npwrapper.libflashplayer.so /usr/lib/mozilla/plugins/
sudo ln -sf /usr/lib/nspluginwrapper/plugins/npwrapper.libflashplayer.so /usr/lib/firefox-addons/plugins/
REMOVE:
sudo rm /usr/lib/mozilla/plugins/libflashplayer.so
sudo rm /usr/lib/nspluginwrapper/plugins/npwrapper.libflashplayer.so
sudo rm /usr/lib/mozilla/plugins/npwrapper.libflashplayer.so
sudo rm /usr/lib/firefox-addons/plugins/npwrapper.libflashplayer.so