This update of Flash Player installer uses the new version 11.2. It downloads it and install.
To install it you must give execution permission:
chmod +x native-64bit-flash-installer-11.2.sh
And then, just execute it:
The installation should be complete without problems.
If you want to install older version take a look at: Install Flash 10 on Ubuntu 64 Bits
Remembering that this is the last Flash version for Linux. Sadly. Security problems will have updates.
EDIT: Update to last Flash 126.96.36.199 (19/10/2012)