Music is a family tradition for pianist Arturo O’Farrill. Son of the late Afro-Cuban jazz trailblazer Chico O’Farrill, the instrumentalist and composer has forged a path of his own as the Grammy Award-winning leader of the Afro Latin Jazz Orchestra. He is also the founder and artistic director of the Afro Latin Jazz Alliance, a nonprofit “dedicated to preserving the music and heritage of big band Latin jazz.” The player’s own children seem to be following in his footsteps: His sons Zachary, a drummer, and Adam, a trumpeter, join him and other musicians onstage this Thursday for a toe-tapping performance at Burlington’s FlynnSpace.