This is not going to happen – flagging is anonymous, after all. As for this particular case, I've talked to the user in question, they claim they where looking for some sort of "dislike feature" :\
I have suggested they post an answer here, but it looks like they have elected not to. And as I said in the comments, at least the "I disagree with this flag" feature has worked just fine in this case.
Regarding the question of some sort of "punishment" for users with many invalid flags, I'm open to suggestions. Here is some data, so we know what we're talking about.
This is a list of chat.SO users (anonymized, of course). The first column is the number of messages the user has flagged. The second colum is the percentage of these flagged messages that where subsequently deleted (either directly by a mod, or they were flagged by enough people). The third column is the percentage of this user's flags that had at least two normal users or one moderator counter-flag (i.e. "I disagree").
The table shows all users that have flagged at least five times, and whose value in the third column is above 50%.
+-------------+-----------+----------------+
| Total Flags | Success % | Disagreement % |
+-------------+-----------+----------------+
| 5 | 0 | 100 |
| 5 | 0 | 60 |
| 13 | 0 | 100 |
| 5 | 0 | 100 |
| 16 | 0 | 100 |
| 18 | 0 | 66 |
| 14 | 7 | 92 |
| 30 | 10 | 90 |
| 33 | 12 | 60 |
| 8 | 12 | 100 |
| 11 | 18 | 81 |
| 61 | 19 | 70 |
| 5 | 20 | 80 |
| 5 | 20 | 80 |
| 7 | 28 | 71 |
| 12 | 33 | 75 |
| 5 | 40 | 60 |
| 5 | 40 | 60 |
| 10 | 40 | 60 |
| 7 | 42 | 57 |
| 11 | 45 | 63 |
| 13 | 46 | 84 |
| 69 | 50 | 63 |
| 8 | 50 | 87 |
| 111 | 50 | 57 |
| 14 | 50 | 85 |
| 17 | 52 | 76 |
| 32 | 53 | 56 |
| 18 | 61 | 72 |
| 8 | 62 | 75 |
| 38 | 63 | 52 |
| 6 | 66 | 83 |
| 6 | 66 | 83 |
| 24 | 75 | 54 |
| 18 | 77 | 66 |
| 10 | 90 | 60 |
| 11 | 90 | 72 |
+-------------+-----------+----------------+
(Many thanks to Senseful for the great table formatter. Oh, and the user that sparked this discussion is the 18/0/66 row.)
Thoughts?