Today I ran Kinsman Ridge Trail from North to South and am posting my time as a current FKT at 5 Hours 4 minutes.
I did not include Mt Moosilauke as it is no longer being grouped with The Kinsman Ridge on the hiking sites. In addition, The Kinsman Ridge Trail switches to The Beaver Brook Trail to continue up Moosilauke and The Kinsman Ridge Trail ends at rt 112 or Kinsman Notch.
Adam Wilcox has a moving time on Strava, which includes Moosilauke, of 5 hours 58 minutes www.strava.com/activities/112474808/segments.
I'm can't tell what his actual time was though and will post it once I contact him.
My moving time was 4 hours 18 minutes which differs greatly from my actual time of 5 hours 4 minutes to do the ridge not including Moosilauke.
I am unaware of any other FKTs on this Ridge, Nothing on web or VFTT site either.