Rinse chicken and pat dry. Place in an 8-inch baking pan and coat with about 2 tablespoons barbecue sauce. Sprinkle with salt and pepper. Bake in a 350° regular or convection oven until no longer pink at the center of the thickest part (cut to test), about 20 minutes. Let stand until cool enough to handle, then tear into bite-size chunks. In a small bowl, mix with remaining barbecue sauce.
Meanwhile, in a 10- to 12-inch frying pan over high heat, stir bacon until browned and crisp, about 5 minutes. With a slotted spoon, transfer bacon to paper towels to drain.
Place pizza crusts on a 12- by 15-inch baking sheet. Spread each with about 2 tablespoons cream cheese. Spoon chicken in sauce evenly over both crusts; top with bacon, green chilies, jack cheese, and hot chili flakes.
Bake pizzas in a 400° regular or convection oven until cheese is browned and bubbling, 15 to 20 minutes. Transfer to a board and cut into wedges.