In a large skillet over medium-high heat, heat 1 tbsp. vegetable oil. Add peppers and onion and season with salt. Cook until soft, about 5 minutes. Transfer to a plate.

Add 1 tbsp. vegetable oil to the pan and heat over medium-high heat. Add chicken and season with chili powder, cumin, oregano, and ½ teaspoon salt. Cook, stirring occasionally, until golden and cooked through, about 8 minutes. Transfer to a plate and wipe out skillet.

Add 1 tbsp. vegetable oil to the skillet. Add 1 flour tortilla to skillet and top half with a heavy sprinkling of both cheeses, ¼ of the chicken mixture, ¼ of the pepper-onion mixture, a few slices of avocado, and a sprinkling of scallions. Fold the tortilla over and cook, flipping once, until golden, about 3 minutes per side.

Repeat with remaining oil, tortillas, chicken, pepper-onion mixture, avocado, and scallions to make 4 quesadillas.

Slice into wedges and serve with sour cream.