In a medium bowl, toss the shredded cooked chicken breast with Buffalo sauce until evenly coated.
Lay one flour tortilla flat and evenly spread a mixture of cheddar and mozzarella cheeses over half of the tortilla.
Top the cheese with a layer of Buffalo chicken and sprinkle diced celery over the chicken.
Fold the tortilla over the filling to create a half-moon shape.
Heat a skillet over medium heat and place the quesadilla on the skillet.
Grill the quesadilla for about 3-4 minutes per side, pressing gently, until the tortilla is golden brown and crispy and the cheese has melted.
Remove from skillet and let rest for a minute.
Cut the quesadilla into quarters and arrange the pieces in a circular pattern on a white round plate.
Place a small bowl of ranch dressing in the center of the plate and add celery sticks on the side for serving.