Combine the shredded chicken and buffalo sauce in a bowl until evenly coated.
Warm a large skillet over medium heat and add the olive oil.
Lay one tortilla in the skillet. Sprinkle a thin layer of cheese over half the tortilla.
Spoon a layer of buffalo chicken over the cheese, add a little more cheese, then fold the tortilla over.
Cook 2–3 minutes per side until golden and the cheese melts. Repeat with remaining tortillas and filling.
Rest 1 minute, then slice into wedges. Top with green onions and blue cheese, and serve with ranch.