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.