Adobe doesn't want (at this time) provide a flash version for linux 64BIT.

• First solution

use a GNU version of flash : gnash . The package is available in synaptic (unlock all ubuntu repersitory ! ), don't forget to install the "mozilla-plugin-gnash". But some flash animations don't work (youtube for exemple).

• Second solution

use nspluginwrapper ( more details here )

In synaptic (or in /etc/apt/sources.list) add this repersitory :
"deb http://janvitus.interfree.it/ubuntu/ edgy-janvitus main-amd64"

Add authentification for this one
#wget http://janvitus.interfree.it/ubuntu/2C4C84CC.gpg -O- | sudo apt-key add -

Update the sources list and install nspluginwrapper package...

Now download the last version of flashplayer9 , uncompress it and CLOSE FIREFOX.
#cd folder-flash
#cp libflashplayer.so /usr/lib/mozilla/plugins
#cp flashplayer.xpt /usr/lib/mozilla/plugins
#nspluginwrapper -i /usr/lib/mozilla/plugins/libflashplayer.so

Normally a file "npwrapper.libflashplayer.so" appears in /usr/lib/mozilla/plugins/
In your home and with your user login create this folder :
$mkdir ~/.mozilla/plugins
And copy npwrapper.libflashplayer.so inside :
$cp /usr/lib/mozilla/plugins/npwrapper.libflashplayer.so ~/.mozilla/plugins

Now start firefox and enjoy...

WARNING :
Sometime after an ubuntu update, firefox freezes everytime with flash, so reuse nspluginwrapper and recopy "npwrapper.libflashplayer.so" in the two folder.
The best solution could be a script...