Flash has been X86_64 compatible for a while now...
sh-4.2$ rpm -q flash-player
flash-player-11.2.202.236-91.1.x86_64
(rpm query on openSUSE Tumbleweed)
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