This seems a reasonable idea to me, perhaps even with a lower threshold than other flags.
The suggestion of flagging as 'Spam' is factually incorrect.
Technically not feasible. We have used all of our custom close reasons (cf previous discussions on adding extra reasons) and I'm not even sure it's possible to modify the flag types.
More to the point: the suggestion remains to use either the spam or rude/abusive flags depending on post content. Both flags will trip automatic removal when 6 such flags are received.
Flags for moderator attention will help if one of us is online but the recommendation as per previous threads remains to use the two main flags above. Close votes shouldn't be used: that's just wasted effort.
No. "Trolling" is a very broad, loaded label with extreme prejudice built into it.
Just as some people will quickly call anyone who bothers them politically either a Nazi or a Commie as an easy way to dismiss them entirely AND vilify them in the same word, I think "Troll(ing)" could also end up as a catch-all close reason that's far too easy to apply, far too damning in effect, far too controversial for other mods to get involved with if they disagree ("and remember, @modXYZ supported trolling!"), and far too hard for the target to defend against.
Your own comment, "perhaps even with a lower threshold than other flags" pretty much confirms what I'm saying here.
You have "Rude/abusive" and "Spam". Those are entirely sufficient.
Edit: It occurs to me that I could offer a descriptive alternative that still satisfies your request while being far less loaded and prejudicial, e.g.: "Encourages non-productive discussion"
Flagging it as spam or rude/abusive is one option, and especially relevant to the more obvious cases.
For cases you think might be trolling, but you're not so sure about, you can alternatively:
Edit it if the question is technically on topic but there are some offensive details that aren't strictly necessary to answer the underlying question or ones that could be replaced with a general summary.
This means taking an attempt at trolling and turning it into a good and useful question that can help others. Alternatively, trolls end up posting such questions in the first place to get past our moderation. Either way, mission accomplished.
Close it if it's not on topic, or it's a duplicate.
Downvote it if you don't feel it's useful. Questions with negative score are less visible on the site and these typically eventually end up getting closed or deleted after a while.
Move on regardless of whether or not you did any of the above. Do not comment. Do not post on Meta about it (you can potentially use a custom flag if you think someone else should take a look at it). Dwelling on it wouldn't help anyone, and you engaging with the post (in a way other than simply casting a vote or flag) is what they want.
For both editing and closing as duplicates, it would help if we actually focus on making reference-worthy questions and answers by removing unnecessary or tangential details from questions and giving more general answers instead of what we're currently doing: focusing too much on the specific details of individual questions, which means there are very few cases of questions that would actually provide an answer to someone having the same problem.