Place a pizza stone or inverted baking sheet on the bottom rack of the oven. Preheat oven to 450 degrees F.
In a small saucepan heat oil over medium-high heat. Add onion, garlic, and salt; cook about 3 minutes or until onion and garlic are tender. Stir in chili powder and cumin; cook for 1 minute more. Remove from heat; stir in beans. Using a potato masher, slightly mash bean mixture. Cook and stir over medium heat for 5 minutes or until thickened and bubbly.
In a medium skillet cook chorizo over medium-high heat about 5 minutes or until fully cooked, using a wooden spoon to break up the meat. Remove skillet from heat and add shredded chicken. Stir to combine.
Working with one tortilla at a time, evenly spread one-fourth of the bean mixture on a tortilla. Top with one-fourthof the chorizo-chicken mixture. Transfer topped tortilla to the pizza stone. Bake for 4 to 5 minutes or until edges are crisp.
Transfer pizzas to a cutting board; let cool for 1 minute. Top with 1/2 cup of the cheese, 1/2 cup of the cabbage, 1/4 cup of the salsa, 2 tablespoons of the cilantro, and 2 tablespoons of chopped red pepper. Repeat with remaining ingredients to make four pizzas total. Cut each pizza into wedges before serving.