apt-get install flashplugin-nonfree
Which is basically a script to download the current version of Flash from Adobe.
apt-get install flashplayer-mozilla
Actually downloads a prebuilt binary and installs Flash to the proper place so it works in all browsers.
Nothing to tweak.
$ apt-cache policy flashplayer-mozilla
*** 2:10.3.181.22-0.0 0
unstable/non-free i386 Packages
Wonders yet again why a distro like Ubuntu which is supposed to be user friendly makes things so complicated.