sh-4.2$ rpm -q flash-player flash-player-11.2.202.236-91.1.x86_64
sh-4.2$ file /usr/lib64/browser-plugins/libflashplayer.so /usr/lib64/browser-plugins/libflashplayer.so: ELF 64-bit LSB shared object, x86-64, version 1 (SYSV), dynamically linked, stripped
I'm not a heavy flash user, but after 6 months I was really frustrated. The 32 bits version works great in comparison.