I seen where a lot of server management companies are charging big bucks for this, so this might save you some time and money.
nano -w /etc/yum.repos.d/dag.repo
name=Dag RPM Repository for Red Hat Enterprise Linux
Then yum update and search for ffmpeg and install all ffmpeg packages including devel.
yum install ffmpeg
yum install ffmpeg-devel
Seems there is some lib problems along the way so in /etc/ld.so.conf
also check /etc/ld.so.conf.d and make sure there are no .conf files that may be loading other files.
To install the php extension follow the simple directions on http://ffmpeg-php.sourceforge.net/
Then you should be all set!