Hello and welcome to the Windows7 forums,
As far as I know, the latest version is 10.0.22.87.
You can check your version by navigating to the C:\Windows\System32\Macromed directory, then right-click on the FlashUtil10b.exe file and choose properties.
You also can go to Tools > InPrivate Browsing and check that. if it's already checked, uncheck it.
And you can go to Page > Compatibility settings and add the site you are trying to view the animation on.