In a mixing bowl, combine the shredded chicken, softened cream cheese, buffalo sauce, shredded cheddar cheese, ranch dressing, and green onions. Mix until thoroughly combined.
Season the mixture with salt and pepper to taste. Adjust the buffalo sauce if you prefer more heat.
Lay one flour tortilla flat on a clean surface. Spoon about 1/4 of the chicken mixture onto the center of the tortilla, spreading it out evenly but leaving the edges clear.
Roll the tortilla tightly from the bottom up, tucking in the sides as you go to create a sealed wrap. Repeat for the remaining tortillas.
Once all the tortillas are rolled, you can choose to slice them into pinwheels or serve them whole. If slicing, cut each roll into 1-inch pieces.
Arrange the roll-ups on a serving platter and garnish with fresh cilantro for an added pop of color. Serve alongside additional ranch dressing for dipping.