How do the mods feel about me flagging questions for closure, even though I would be able to VtC myself, if I weren't already out of votes?
Generally, as a user with the privilege to vote to close, you should only use moderator flags in cases where the community cannot vote to close (e.g. if the question is locked or bountied), or where a question is too old or inactive to gain enough community votes to be closed. A moderator is better equipped in such cases, as we can work with locked questions, remove bounties on inappropriate questions, as well as close and reopen questions with a single vote.
It's a bad idea to use moderator flags simply to escalate your close votes, or to supplement your limited number of close votes. Especially so on newer questions — the site gives members a set number of close votes each day for a reason.
Related: How do the mods feel about me flagging a question for closure (a super obvious code-dump, for example), even if I have CVs remaining, in an attempt to preserve my close votes for less clear cut close decisions?
At least on Stack Overflow, we have an immense community to help regulate questions, and that means more than enough community votes to go around. If you feel that a question is blatantly off-topic, chances are it'll be closed by other users fairly quickly so you don't need to cast a vote if you don't want to waste it, but if you spot it again and it's still open, perhaps it'll be a good idea to cast your own vote. It's usually not necessary to raise a moderator flag in such a situation.
I'm saying this not only because it's how it's supposed to work, but also because it actually works; a lot of the time, when we receive custom flags accompanying close votes, odds are by the time we get to them the questions have already been closed by community votes. That leaves us with a dud flag that we can't do anything else with but whisk away. This seems pretty simple and mundane, but given the large volume of flags we have to deal with on a regular basis, it can get frustrating. In fact, we've adopted the practice of declining custom flags that accompany close votes; see this other question for further reading.
If you must flag a new question for immediate removal, make sure to explain to us why exactly this process needs to be expedited. If a question is spam or offensive, use the appropriate red flag. Whether it seems to be a troll or something else just isn't right, definitely bring it up as that is the kind of thing we definitely want to look at.