Long story short: since custom flag responses are messages to users like any other (answer, comment, suggested edit, chat message etc.), users should be notified about them!!
A problem I have with flagging, as it currently functions, is that flaggers are not notified about custom responses to flags, when they are given. I really don't care if I don't find out about every last flag of mine, whether it was marked "helpful" or not, but if a moderator went to the effort of typing out a custom response to my flag, explaining why it was or was not helpful, I'd like to see that response.
The logical place for this response would be in the messages inbox (the red number thingy in the top left corner), where other responses to user actions (like answers, comments, edits, and chat messages) go.
This may also help to alleviate Monica's problem of users not realizing that their flags go somewhere -- while I agree with her that "We shouldn't send notifications for [all] flag responses; that would be way too noisy for a lot of people," I think that in the event of a custom response, the flagger should be notified (because some mod thought that this information was relevant to the flagger), and it would not be too noisy because (in my experience1) most flags do not receive a custom response.
This could provide one way that flaggers can be made aware of their flagging history.2
1 I don't know who can see this, but my flagging history on Mi Yodeya, to date, is 55 flags total (49 helpful), and only one custom response (....that I didn't see for a while, till I checked my flagging history for a different reason).
2 While I don't think that this will replace Monica's suggestion entirely, it would certainly help it a little.
To give credit where credit is due, while I came up with this idea myself, I did notice that someone else had posted about a similar idea earlier in a comment to Monica's question.
Edit: Just spotted this question from the related questions along the side of the page; note that while that proposal is similar to this one, it was about sending all declined flags to the inbox, while I suggested that only the ones with custom responses should make it to the inbox.