Make the taco seasoning: Mix all of the ingredients with 1 tablespoon each salt and black pepper in a bowl.
Prepare the pizza: Mix 2 tablespoons of the taco seasoning and the canola oil in a shallow bowl. Pound the chicken between 2 pieces of plastic wrap to 1/4 inch thick. Add the chicken to the bowl, turning to coat, and marinate 30 minutes.
Preheat a grill to medium high. Grill the chicken until cooked through, about 4 minutes per side. Let cool, then cut into bite-size pieces.
Divide the dough into 3 pieces. Roll out each on a floured surface into an 8-inch round. Brush with canola oil, sprinkle with taco seasoning and grill until crisp, 3 to 5 minutes per side; remove from the grill.
Mix the cheeses in a bowl, then sprinkle on the crusts and top with the chicken. Return the pizzas to the grill, and cook until the cheese is melted, about 5 minutes. Meanwhile, mix the avocado, lime juice, cumin, chili powder, red onion, and salt and pepper to taste. Top the pizzas with the avocado mixture, salsa, sour cream and cilantro.