I don't know the exact thresholds, but [flagged] happens at some # of flags, and [dead] happens at a higher # of flags. [flagged] are de-ranked, but not made invisible or unavailable for replies like [dead] are. I guess the recourse would be upvoting - I think those counteract flags in terms of ranking. I don't know if that would do anything to remove the [flagged] display, though.