Melt butter in a large soup pot over medium heat. Add onion, celery, and carrots, season with salt & pepper, then saute until tender, about 10 minutes. Add garlic and thyme then saute for 1 more minute. Add chicken broth then increase heat to high and bring to a boil. Add chicken breast halves and cook until no longer pink in the center, about 10 minutes, then remove to a plate and set aside. Shred when cool enough to handle. Add wild/brown rice blend to the pot then place a lid on top, turn heat down to medium-low and simmer for 40-50 minutes or until rice is tender. In a small bowl, whisk together 1/4 cup milk with flour until smooth then add remaining milk. Slowly drizzle into soup while stirring. Add chicken then simmer soup for 10 more minutes uncovered and serve.