Melt butter in a large Dutch oven over medium-high heat; add chicken and next 3 ingredients, and saute 10 minutes. Stir in broth and next 3 ingredients.
Bring to a boil; reduce heat, and simmer, stirring occasionally, 20 minutes. Stir in 2 cans of beans and chiles.
Mash remaining can of beans in a small bowl. Whisk together flour and milk, and stir into beans. Gradually add bean mixture to soup mixture, stirring constantly. Cook 10 minutes or until thickened. Remove from heat, and stir in cilantro. Serve with desired toppings.