I've just passed the threshold for being able to vote to close on another SE site. Some of the questions I flagged prior to having this privilege are still in the review queue because not enough votes have been cast to close them yet (it's a much smaller site than SO).
It seems that once you have the close vote privilege, any flags-to-close you make after that are converted to votes-to-close. However, it's not clear whether this is retroactive and applies to the still-open flags I raised before getting this privilege.
When I go to the close vote review queue, these questions are still visible in the queue. Then when I click on "close" to agree with the close vote it says "You already flagged this question for closure". Searching on meta reveals that this (IMO very confusing) wording is because once you have privileges close votes and flag-for-closures are counted the same.
However, it's still not clear whether the old flags are converted to close votes. This is quite confusing.
So here's my suggestion.
If the flag that I cast when I did not have privileges to vote to close has not been retroactively converted to a close vote (which seems more likely) then I should be allowed to cast a close vote.
If my previous flag does now count as a vote, I think this should be worded more clearly: You already voted to close this question (as opposed to You already flagged this question for closure) and/or make it not appear in my close vote queue to begin with (since I've already voted and it won't let me vote again).