I just installed Fedora 15 (Desktop i.e. standard) 64 bit and here is how I installed Adobe Flash Player 11b1 64bit version. I launched terminal and typed in the following commands.
su -c 'yum install wget' cd /tmp wget http://download.macromedia.com/pub/labs/flashplatformruntimes/flashplayer11/flashplayer11_b2_install_lin_64_080811.tar.gz tar xzvf flashplayer11_b2_install_lin_64_080811.tar.gz su -c 'cp libflashplayer.so /usr/lib64/mozilla/plugins/' su -c 'cp -R usr/ /'
Then I restarted Firefox and Flash player is working.
Note: This does not work for 32 bit version of Fedora. For 32-bit version, try this:
su 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 yum update yum install flash-plugin
Hope this helps.