To clarify, Windows 7 64-bit runs 32-bit software. For instance, the web browser you're using on it is likely a 32-bit executable. There are 64-bit web browsers available, but not really for Windows, and even then there is no version of Flash that supports them.
You don't need to be looking for 64-bit programs for your PC since it is backwards compatible with the older ones. It's just that it doesn't work the other way around.