Make sure everything (FLMM, for example) is running as Administrator. I originally had some problems because things which were set to run as Admin were changed to not.
Best way I've found is to right-click on FLMM and run as administrator.
After FLMM is running as admin, then you can double-click on the mod file to extract it to FLMM.
After mod file is extracted, you can activate the mod.
Everytime you want to deactivate or activate a different mod, run FLMM as an administrator. I never could get the check-box "Run as admin" to stay, so I just right-click and choose from the popup menu each time.