64-bit Windows 7 comes with both 64-bit and 32-bit Internet Explorer, but there's no 64-bit version of Flash, so it won't work in the 64-bit version of IE. If you want to use flash you have to use the 32-bit version.
You can find the 32-bit version of IE as follows:
-> Click Start
-> Type "Internet Explorer" in the "Search" box
-> Click the "Internet Explorer" link (not "Internet Explorer (64-bit)") near the top of the search results.