Preheat the oven to 425°F (220°C).
In a large bowl, combine the shredded chicken, sliced red bell pepper, sliced green bell pepper, and sliced onion.
Add olive oil, ground cumin, chili powder, garlic powder, smoked paprika, salt, and black pepper to the bowl. Toss everything together until well coated.
Line a large sheet pan with parchment paper or lightly grease it with cooking spray.
Place two flour tortillas flat on the sheet pan.
Evenly distribute half of the chicken and vegetable mixture over each tortilla.
Sprinkle half of the shredded cheddar cheese and half of the shredded Monterey Jack cheese evenly over the chicken and vegetables on each tortilla.
Top each with the remaining two tortillas, pressing down gently to form quesadillas.
Lightly spray the tops of the quesadillas with cooking spray to help them crisp up.
Bake in the preheated oven for 12 to 15 minutes, or until the tortillas are golden brown and the cheese is melted.
Remove from the oven and let the quesadillas cool for 2 minutes before slicing into wedges.
Serve warm with your favorite salsa, sour cream, or guacamole.