Note: I am not referring to flagging; I am referring to voting to close a question. Who has the privilege to vote to close doesn't use flagging, except if the question is spam. The purpose of the proposed badge is not encouraging users to flag, but encouraging users to vote to close, which is quite different.
As incentive for voting to close questions, I was thinking of a badge given to the first user who votes to close, when X% of the questions s/he voted to close have been closed. For example, if only 10% of the questions the user voted to close are closed, then the badge should not be given to the user.
The badge could be an incentive to vote to close, but as the badge is given to the first user who votes to close, there should not be an increment of wrongly closed questions.
There could be a silver badge, and a gold badge.
I didn't think for how much closed questions the badge should be gained. To decide that, we should look at the number of questions a user normally vote to close, and how many of those questions are really closed.
If the definition of the badge is not too restrictive, then questions that are re-opened after Y days should not be considered.