You can't install a 32-bit flash player in a 64-bit browser. But why are you using a 64-bit browser? The default installs of both IE and Firefox are 32-bit even on a 64-bit OS. You would have to have specifically chosen to install or use a 64-bit browser.
Les J: "64bit computers come with 64bit Internet exporers and other 64bit programs" Yes, you are correct. Every 64-bit installation of Windows Vista comes with a 64-bit installation of Internet Explorer. However, using it is not the default. The default is the 32-bit version. You would have to specifically chose to run the 64-bit version of IE. Similarly, if you install Firefox, it will install the 32-bit version unless you specifically chose the 64-bit version.