In a large bowl, combine the shredded chicken and buffalo sauce. Mix well until the chicken is fully coated.
In another bowl, mix the cheddar cheese, mozzarella cheese, and cream cheese until well combined.
Heat a large skillet over medium heat and add the olive oil.
Place one tortilla in the skillet and spread a portion of the cheese mixture over half of the tortilla. Top with a portion of the buffalo chicken mixture and sprinkle with green onions if using.
Fold the tortilla in half and cook for about 3-4 minutes on each side, or until the tortilla is golden brown and the cheese is melted. Repeat with the remaining tortillas and filling.
Cut each quesadilla into wedges and serve warm with sour cream and ranch dressing.