In a large bowl, beat the softened cream cheese until smooth using a hand mixer or a strong spoon.
Add the shredded cheddar, Buffalo sauce, blue cheese crumbles, chopped chives, garlic powder, onion powder, salt, and cracked black pepper to the cream cheese and beat until well combined and creamy.
Fold in the shredded cooked chicken by hand until evenly distributed through the mixture.
Lay a flour tortilla flat and spread an even layer of the chicken mixture over the surface, leaving a small border at the edge; repeat with remaining tortillas.
Tightly roll each tortilla into a log and refrigerate for 5–10 minutes to firm up for easier slicing (optional).
Using a sharp knife, slice each roll into 1-inch thick pinwheels and arrange on a serving platter.
Serve with blue cheese dressing and extra Buffalo sauce for dipping.