Though he is thought of as a folk musician in some circles and probably should not, guitarist John Fahey loved traditional jazz and featured it on his albums Of Rivers and Religion, After the Ball, and Old Fashioned Love. The last one, OFL, has a great tune by Clarence Williams, Boodle Am, as well as a jazz Keep Your Lamps Trimmed and Burning.
Then you might think of the early jazz blues singers like Bessie Smith and that crowd having some connection with the folk music of the day, but I might be wrong.