Melt butter in large stockpot over medium heat. Add diced carrots, celery, and onion. Stir to coat with butter, and allow to cook while cutting chicken.
Add chicken, salt, garlic powder, and pepper. Stir fry 3-5 minutes until outside of chicken is mostly cooked. Sprinkle with flour and stir to coat.
Slowly pour in chicken broth while stirring to keep mixture smooth. Bring to boil, and stir in rice.
Reduce heat to medium-low, cover, and cook the recommended cooking time for your choice of rice (usually 30-40 minutes).
Remove cover, and taste rice to be sure it is cooked completely (if not, continue cooking a few more minutes). When rice is done, stir in milk, and return heat to medium. Bring to a low boil, and simmer soup a few more minutes until heated through. Add additional salt and pepper to taste.