Don't confuse a 64bit OS with a 64Bit
[COLOR=blue ! important][COLOR=blue ! important]application[/COLOR][/COLOR].
Any 32bit app can still run on a 64bit OS, but IE8 has a 64Bit version that is the default in Win7.
Firefox is 32bit, so of course Flash will install properly. If you look in the program list for Win7 you will see 2 versions of IE8, 64 and 32 bit. Run the 32bit version and install Flash, then you will be able to see flash video.
Just think of it this way, the OS is the plate and the application is the food. You are using a big plate but the waiter can only bring you small portions of Flash on a saucer.