Falkner received his education at Peterhouse, Cambridge, where he graduated B.A.
On 23 July 1679 he was collated by the Bishop of Ely to the rectory of Glemsford, Suffolk.
[1] He was also town preacher at the chapel of St. Nicholas, King's Lynn, where he died on 9 April 1682.
By his wife Susan, daughter of Thomas Greene, merchant and alderman of Lynn (who died on 30 August 1680), he had several children.
He was a learned champion of the Church of England.