Are you trying to do it while import the costume while in the initial character creator? 'Cuz I know that has never worked for me. Just go to the costume vendor first chance you get, and it should import just fine from there.
If that's not the issue, I don't know. Are you sure that there are costumes saved in the right game folder? (By the way it's: <Star Trek Online directory>/Star Trek Online/Live/screenshots)
On the first tailor screen (the one with the outfit previews), the "Load Outfit" button next to the "Exit" button is always grayed out. Click the "Modify" button to edit a costume. Then, click the "Load Outfit" button below "Head", "Body", and "Uniform" tabs; that button should work.