If you're using jnovy's TeX Live 2011 packages for Fedora 16, then yes, there is an animate package. Go to http://jnovy.fedorapeople.org/texlive/packages.fc16
and scroll down to see the following packages, which you can download from that page:
texlive-animate-2011-8.svn24901.noarch.rpm 15-Jan-2012 14:36 27K
texlive-animate-doc-2011-8.svn24901.noarch.rpm 15-Jan-2012 14:36 2.7M
If you're using the default TeX Live 2007 packages for Fedora 16, then you may be out of luck. I really think that in Fedora you are better off just installing TeX Live from the official iso image file
. It helps to avoid a lot of problems, plus it lets you use tlmgr for updating (which is the preferred way).