Current UX for NAA and VLQ flags is long obsoleted by various changes in flagging process. Suggested feature offers an opportunity to correct this and bring it more in line with ideas laid out in Stack Overflow is not yet a vast wasteland: a history of moderator tooling.
To see why it is so, take a closer look at what SE team folks recommend in another answer:
leaving a comment... gives the author a chance to correct the problem in addition to offering mods and reviewers a better understanding of what you found concerning... And if you're wrong, someone might tell you that...
If you think of it, recommending to use comments is a fascinating advice. 3-4 years ago, it would be totally opposite to that, "Don't ever use comments to back up NAA / VLQ flags. If you feel a need to explain something, just use custom flag. Don't expect moderator to waste their time trying to find your comment and figure if it relates to flag or not."
- This is a radical change in flagging workflow, and as you can see, SE folks openly endorse it (and there's likely no way back, if you check that "not yet a vast wasteland" post referred to above).
The reason for such a striking change is that nowadays NAA / VLQ flags target totally different audience who are expected to handle them in a very different way.
As opposed to diamond moderators, LQ reviewers are expected to invest substantial effort in studying flagged post if needed. This is because, as opposed to moderators, they can't be trusted to make right decisions quickly. Also, as opposed to moderators, they are expected to have plenty time for that - at the limit of 20 reviews a day and thousands other eligible users to back up if they choose to skip review, why wouldn't they.
This change of the audience led to the change of the role of comments. These are now welcome as sort of grease, helping reviewers - regular inexperienced users - better understand what's going on there and make the system work smoother and more reliably. (Compare that to the past, could you ever imagine self commenting to explain routine VLQ / NAA to a veteran moderator who was handling hundreds such flags a day?)
Okay, now that we learned that comments are assumed to integrate with VLQ/NAA flagging workflow, let's see if it makes sense to improve this integration.
For that, consider a pretty similar system that also involves communicating moderation details to multiple, possibly inexperienced reviewers. I am talking about close voting and more specifically, about free-form close reasons:
Closers can enter a free-form reason... Free-form reasons will be presented as comments, but the close dialogue will refer the reader to the comments for more info...
This is how it looks like for close vote reviewers:
You see, free-form close reasons are in essence regular comments, only with additional integration into close dialog. That integration (copying comment text into close dialog) makes pretty good sense, as it spares close vote reviewers the need to look for and figure whether particular comment relates to the vote or not (not to mention protection it offers for the cases of regular comments being edited or deleted or obscured by other comments).
Same approach, and for the same reasons, could be (and I believe should be) implemented for flagging. (side note, since it involves comments, it makes sense to consider limiting an option to cast "commented flags" to users having a privilege to comment)
If flag messages get implemented as "connected comments", similar to free-form close reasons, one can even argue that this doesn't introduce changes to flagging process - because, as explained above, change already occurred long ago and is even openly endorsed by SE team.
From this perspective, such a feature can be considered simply as an improvement to already established workflow, making it smoother and less error prone.