In a 6-quart slow cooker, stir together chicken stock, onion, carrots, celery, wild rice, salt, pepper, mushrooms, and garlic. Nestle in the chicken, thyme, and bay leaves. Cover and cook on low until chicken and wild rice are tender, about 7 hours.
Remove chicken from the slow cooker. Increase heat to high. Shred chicken; set aside. Discard thyme sprigs and bay leaves.
In a medium bowl, whisk together milk and flour. Stir into stew. Cook on high until thickened, about 10 minutes. Gently stir in chicken. Garnish with parsley, if desired.