Interesting. The most obvious option would seem to be to (like we do on SO), track the success of people's flagging, and essentially mute them if they are consistently flagging inappropriately.
That is the simplest option I can think of - but I'm open to others?
As an update on this event - I can see the flags in question, 15 each by two users on the same IP. I'm sure it is an absolute coincidence that this was 15 flags in 25 seconds by the first account, then 3 minutes (shall we estimate: time enough to either log out and back in, or lean over to somebody in the next pod), and another 15 flags in 30 seconds.
Because of this - a more obvious and immediate strategy may be rate limiting. Flagging 2 things at around the same time makes sense, but this? This is clear abuse.
See More information is needed in chat Flagged Posts for the current set of changes.