As this answer:
If you have the privilege to cast close votes, it doesn't matter at all if you do it via the 'close' link or via the 'flag' link and the option 'Should be closed ...'. It will count as a close vote, not a flag. The 'close' link is just a 'shortcut' for an action which is quite often necessary.
If you don't have the privilege, then you don't see the close link at all. Flag -> 'Should be closed ...' will count as a flag, not a close vote.
Recently I got access to the
close link and I still have access to the
flag link. It makes me befuddled to choose which one if I find a problematic question. I think the SE should remove "flag" for users that reached +3k reputations.
Why should I flag it if I have access to vote to close a question?