There are a good number of instructions in here for this.
I just use the YUM option in Adobe page
after you install it, maybe like
#yum -y localinstall adobe-release-i386-1.0-1,noarch.rpm
(# means you're root)
or something like that
then you have to do a system update and accept the Adobe key for the repo
then you have to install the program, flash plugin
I usually use yumex so I can find it or I guess you could
#yum -y install flash-plugin
I think that will work
I'm experimenting with the 64 bit version. All I did was dl it and copy it to
~/.mozilla/plugins ( I think that's it )
(~ means your home folder /home/myusername/...)
but I'm the only user on this box and I'm not sure it really works, I've had this up for a while and it's starting to look like a High School lab frog.
You have to get the 64 bit version here