Heat the oven to 400°F. Lightly grease 8 cups of a standard muffin tin.
In a large mixing bowl, combine the ground chicken, egg, oats, diced celery, green onion, garlic powder, salt, black pepper, and 2 tablespoons of the buffalo sauce. Mix gently until just combined.
Divide the chicken mixture among the 8 prepared muffin cups. Press it lightly into each cup without packing it too firmly.
Bake for 18 minutes. Carefully spoon the remaining buffalo sauce over the tops, then bake for 5 to 8 minutes more, until the muffins reach 165°F in the center.
While the muffins bake, whisk the mayonnaise and apple cider vinegar in a medium bowl. Add the sliced celery and shredded carrots, then toss to coat.
Let the muffins rest in the tin for 5 minutes. Serve them warm with the celery slaw.