Preheat the oven to 350 degrees F (175 degrees C). Lightly grease a large baking dish.
Melt butter in a medium saucepan over medium heat. Sauté green onions in hot butter until tender, 3 to 4 minutes.
Add garlic powder, then stir in condensed soup, green chiles, and sour cream. Mix sauce until well combined. Reserve ¾ of the sauce in a bowl and set aside.
Add chicken and ½ cup cheese to remaining sauce in the pan; stir until cheese is melted.
Fill each flour tortilla with chicken mixture and roll up. Place seam-side down in the prepared baking dish.
Stir milk into reserved sauce in the bowl and spoon over rolled tortillas. Top with remaining ½ cup cheese.
Bake in the preheated oven until cheese is bubbly, 30 to 35 minutes.
