The reason why you still see a
flag link after gaining the close questions priviledge is that there are other reasons you may want to flag for than closure. However, Stack Exchange wanted to keep the opening dialogue as identical as possible, probably due to reasons.
flag dialogue is still helpful to mark spam (flag spam, close later if at all), offensive posts (flag, close later if at all) and whatever may require moderator attention.
The other options (duplicate and should be closed) will just link you forward to your close vote dialogue silently, as JoErNanO explained. The underlying philosophy is that SE is user moderated, so if you can close you should. There is no chickening out like ‘maybe this should be closed, but I am not sure.’
Irrelevant side note: My most popular flag by a very significant margin across all my Stack Exchange accounts is
obsolete comment ;)