You're probably trying to use the 64-bit version of Internet Explorer. Since Adobe Flash only comes in 32-bit versions it won't install inside 64-bit IE.
The solution is simple: use 32-bit Internet Explorer. There should be items for it in your Start Menu - 64-bit IE is definitely listed as "Internet Explorer (64-bit)", so "Internet Explorer" or "Internet Explorer (32-bit)" is what you want to use.