The most current version of Flash for Linux is version 7.0 while Windows users are already on 8.0. However Macromedia has officially stated that there will be an upcoming version 8.5 for Linux. However it will be shipped after the Windows version becomes available. Even though that post states that no 64bit version is being planned, another engineer has stated that there is some work being done towards a 64bit version.
In the end, it’s good news to see Macromedia/Adobe putting forth some effort to support Linux .