Adobe has a repository to install the flash plugin using yum. Install the repository:
rpm -ivh http://linuxdownload.adobe.com/adobe-\ release/adobe-release-i386-1.0-1.noarch.rpm
Import the key:
rpm --import /etc/pki/rpm-gpg/RPM-GPG-KEY-adobe-linux
yum the software:
yum install flash-plugin libflashsupport
Now you would ask me why install libflashsupport. If you don’t you will have no sound when playing Flash in your web browser.
Update: You no longer need to install libflashsupport.
PS: For Newbies please make sure you are executing these commands as a root user, otherwise it will not work