See if this article gives you more information: http://helpx.adobe.com/flash-player/release-note/readme-flash-player-linux.html
Please feel free to ask for clarification, if needed - I'm sure someone here knows something about Linux (sorry, I don't).
I tried downloading the 64 bit ubuntu, but the window that comes up asks me to choose and application with which to open it. When I check the "Installation Instructions" on http://helpx.adobe.com/flash-player/release-note/readme-flash-player-linux.html I simply don't understand the first two steps... "Unpack the plugin tar.gz and copy the files to the appropriate location." I don't know where the appropriate location would be, I just.. don't get it. I don't even know how to "unpack" a file... I'm really sorry, I appreciate your help, but I'm so clueless to all of this. I don't know where to begin.
I really don't know anything about Linux, so it would be best to wait for an expert to come and help you; hopefully after this weekend is over.
But I remember one week ago I had to use some Linux version on my system (to recover a hard drive). While I was waiting I tried to install Flash Player. Unpacking install_flash_player_11_linux.x86_64.tar.gz was quite easy, but I don't remember exactly how I did it - right-click, perhaps?
The target location, according to the instructions, appears to be /home/<user>/.mozilla/plugins/