In a large skillet over medium-high heat, warm 1 tablespoon of vegetable oil. Add the sliced bell peppers and onion, seasoning them lightly with kosher salt. Sauté the vegetables until they become tender, about 5 minutes. Transfer the cooked vegetables to a plate and set aside.
In the same skillet, heat another tablespoon of vegetable oil over medium-high heat. Add the chicken strips and season with chili powder, ground cumin, dried oregano, and ½ teaspoon of salt. Cook the chicken, stirring occasionally, until it turns golden brown and is thoroughly cooked, approximately 8 minutes. Transfer the chicken to a plate and wipe out the skillet.
Pour 1 tablespoon of vegetable oil into the skillet and place one flour tortilla in the pan. On half of the tortilla, generously sprinkle a mix of Monterey jack and cheddar cheeses. Add a quarter of the cooked chicken, a quarter of the pepper-onion mixture, a few avocado slices, and a sprinkling of thinly sliced scallions. Fold the other half of the tortilla over the fillings and cook, turning once, until both sides are golden brown, about 3 minutes per side.
Repeat the process with the remaining oil, tortillas, chicken, pepper-onion mixture, avocado, and scallions to create four quesadillas in total.
Cut the quesadillas into wedges and serve them hot with a side of sour cream for dipping. Enjoy your delicious homemade chicken quesadillas!