Flash is very easy to install. Forget about packages, installers, blah, blah. Just download the tar.gz for Linux file from http://get.adobe.com/flashplayer/?promoid=BUIGP
. Close your open browsers. Once the file is downloaded, open a terminal, su to root, start Midnight Commander (mc) and go to your user download directory. In Midnight Commander, highlight the downloaded Flash file, hit F2, and select Unpack Selected File. The one you want is libflashplayer.so; ignore any others. Still in Midnight Commander as root, switch the other panel to /usr/lib/mozilla/plugins. Find the libflashplayer.so in that directory and rename it to libflashplayer.so_old. (This makes it easy to recover if the new Flash Player causes problems.) After the file is renamed, copy libflashplayer.so that you just unpacked from the download directory to /usr/lib/mozilla/plugins. Make it executable (in Midnight Commander, highlight the file and hit Control+x, c and put checks in the Execute, Search boxes). I always do a ldconfig at a terminal prompt every time I install something but it's probably unnecessary.
When you restart your browsers, they should all be using the new version of Flash. Firefox, SeaMonkey, and Opera all can get Flash from the /usr/lib/mozilla/plugins directory. You don't need to install into each browser individually.
To make sure your browsers are using the new Flash, go to http://www.adobe.com/software/flash/about/
and you'll see what version you are running and what the latest version is.
When everything is working, you can delete the files you downloaded and unpacked from your user downloads directory.