Found bapt in NYCRO; Askrigg bapt; John, bapt 11 May 1678, son of John Kilburne of Worton. This would make him illeg, but on IGI it says 1679 so have changed to that. Backed up by Michelle Chamberlain info.
A John Kilburne married Ann Forsett in Whitkirk (nr Darlington) 22 Jun 1689, this could well be our chap.