Combine the onion, carrots, celery, chicken, wild rice, mushrooms and thyme in the slow cooker. Add the chicken stock. Cover and cook on high for 5 hours.
Add the milk, and cook for 1 additional hour.
In a small saucepan over low heat, melt the butter. Add the flour, and stir constantly, about 2 minutes. Add 1 cup water, and stir to combine. Add the butter-flour mixture to the soup. Salt and pepper, to taste. Stir to combine well. Cover and allow soup to finish cooking in the slow cooker.
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