I could be convinced to jump on board a Burnes trade but I would want a mlb ready bat and rotation piece.
Manzardo, Montgomery, and Basabe would be pretty good. I would definitely try for Junior Caminero ( not that he is mlb ready. Would Junior Caminero, Luke Raley, and Luis Patino work. Maybe trade for a starter like Giolito to make up for missing out.
I still think the Rangers would be the best fit. They have 3 or 4 hitters of interest and a couple young pitchers. Justin Foscue, Jack Leiter, and Owen White for Burnes and a reliever. (Not real high on Ezekiel Duran but he could work).
Dodgers also of course Busch, one of their 3 or 4 young starters, and a 3rd AA starter