If you play around with Google Maps Street View you can see that Kings Highway is paved as it leaves Stoddard but at some point appears to become dirt:

https://www.google.com/maps/@43.0985...!7i3328!8i1664

How long the unpaved stretch is is not known.

King's Highway ends at Faxon Hill, which is paved to NH 31, but it looks in rough shape. However, the image is from 2009. Maybe it's been resurfaced since then.