No source independent of Nyingma tulku-lineage tradition records when Karma Lingpa was born or died. The commonly repeated dates of 1326 and 1386 come from later biographical and lineage compilations rather than from any record contemporary with him.
What would resolve this A Tibetan document contemporary with Karma Lingpa, distinct from the later tulku-lineage biographies that supply his conventional dates, naming a year for his birth or death.
OpenTibetan Buddhist studies, history of the Nyingma tertön traditionBryan J. Cuevas, The Hidden History of the Tibetan Book of the Dead