In a medium bowl, combine the shredded chicken with buffalo wing sauce and cream cheese, mixing well until fully incorporated.

Chop the celery and green onions finely, then fold them into the chicken mixture along with the shredded cheddar cheese.

Lay out each flour tortilla flat on a clean surface to prepare for assembly.

Evenly spread the chicken mixture over each tortilla, leaving about an inch border around the edges.

Carefully roll each tortilla tightly from one end to the other to form roll ups.

Place the roll ups seam-side down on a baking sheet and bake in a preheated oven at 375°F (190°C) for 8-10 minutes until warmed through and cheese is melted.

Remove the roll ups from the oven and let them cool slightly before slicing into 1-inch pieces.

Serve warm with ranch dressing on the side for dipping and garnish with chopped parsley or cilantro if desired.