Personally, my feeling is that these kind of massively long comment threads never come to any good.
I had one of them the other week, it also came to no good.
The thing is if User X and User Y hold contrary opinions really strongly, long comment threads will never be able to sort them, they are too intricate and our comment UI sucks at discussion. It was not designed for it.
Personal attacks are never acceptable and should be flagged, but please keep in mind that your dispute will most certainly not be resolved in a comment thread and will very often escalate. When people get emotional about stuff they sometimes slip.
To answer the questions.
In general, is this an appropriate use
of flagging comments?
Yes, flag comments that are personal attacks.
Are these specific comments over the
line? If not, what is the line?
The line I think is - is this discussion, does it belong in the upcoming 4th place?
Are there other (better) ways of
dealing with this situation?
Yes you can not win all the battles, be mindful that long comment threads very often come to no good, just let it go early before it escalates.