Yes, the 32 bit flash plugin (i386) won't work in a 64 bit browser. You need the
64 bit plugin.
I used it for a while, but certain web pages caused Firefox to crash, so I don't use it anymore, will try again when it's not alpha. But it don't hurt you to try it.
I noticed you only have one post, so I'll assume your a newbie. So...
It says to unpack the tar.gz file and what you'll get is a "libflashplayer.so" file, you have to enable viewing hidden files in your home directory, there you will see a folder called ".mozzila", in that folder there needs to ba a folder called "plugins", if it's not there create it and put a copy of the "libflashplayer.so" file in it.
If you're doing it all from command line, type:
ls -a from your home directory to see all files and directories including hidden ones.