Heat the olive oil over medium heat in a medium skillet. Add the onions and sauté for 3-4 minutes. Add the chicken and continue to sauté, stirring in 1/3 cup barbecue sauce, until the chicken is cooked through, about 6-7 minutes.
Place the pizza crust(s) on a baking sheet or pizza stone. Spread with the remaining 1/3 cup barbecue sauce. Top with the chicken and onion mixture. Top with the shredded cheeses. Bake for 10-12 minutes, until the cheese is bubbling. Top with crushed red pepper flakes to taste, if using, and serve.