Preheat oven to 350°F.
Arrange tortillas in a single layer on a baking sheet and coat on both sides with cooking spray. Bake, flipping once, until crispy, about 12 minutes.
Meanwhile, heat chicken tinga and refried beans in separate pans until steaming. Divide the beans among the tortillas, then top each with 1/3 cup chicken and 1 tablespoon each cheese and cilantro.