In a slow cooker, place chicken breasts on high heat for 1 hour. The chicken will be done when it is easy to shred.
In a Dutch Oven, melt the butter. Add the celery, carrots, onion, garlic, thyme, sea salt and black pepper. Cook over moderate heat, stirring occasionally, until the vegetables just start to soften, about 10 minutes. Sprinkle the flour over the vegetables and cook, stirring, until evenly coated and lightly browned, about 3 minutes.
Add in the bone broth, whole milk, and heavy cream. Bring to a boil, then simmer over moderately low heat, stirring occasionally, until the vegetables are tender, about 30 minutes.
Add the chicken and wild rice and simmer, stirring occasionally, until the wild rice is tender. About 30 minutes.
Ladle the soup into bowls and serve. Enjoy!