1. Change Root User

sudo -i
## OR ##
su -

2. Install Adobe YUM Repository RPM package

## Adobe Repository 32-bit x86 ##
rpm -ivh http://linuxdownload.adobe.com/adobe-release/adobe-release-i386-1.0-1.noarch.rpm
rpm --import /etc/pki/rpm-gpg/RPM-GPG-KEY-adobe-linux

## Adobe Repository 64-bit x86_64 ##
rpm -ivh http://linuxdownload.adobe.com/adobe-release/adobe-release-x86_64-1.0-1.noarch.rpm
rpm --import /etc/pki/rpm-gpg/RPM-GPG-KEY-adobe-linux

3. Update Repositories

yum check-update

4a. Install Adobe Flash Player 11.1 on Fedora 16/15/14/13/12, CentOS 6.2/6.1/6/5.7 and Red Hat (RHEL) 6.2/6.1/6/5.7 Fedora 16/15/14/13/12, CentOS 6 and Red Hat (RHEL) 6 32-bit and 64-bit version

yum install flash-plugin nspluginwrapper alsa-plugins-pulseaudio libcurl

4b. Install Adobe Flash Player 11.1 on CentOS 5.7 and Red Hat (RHEL) 5.7 CentOS and Red Hat 32-bit and 64-bit version

yum groupinstall "Sound and Video"

yum install flash-plugin nspluginwrapper curl

5. Verify that the Flash Player Plugin is working

Open Mozilla Firefox and write about:plugins on address bar. Results 
should look like following:
Adobe Flash Player 64-bit installed on Fedora 16 64-bit (x86_64)