Combine broth, salsa and flour in a slow cooker, whisking to blend. Stir in onion, then arrange chicken in the pot, smooth side up. Cover and cook on low for 6 hours.
Remove chicken-breast halves to a plate. Ladle sauce from pot into a blender and puree. Stir in sour cream. Return sauce and chicken to the pot. Keep warm until ready to serve.
Arrange chicken on plates and top with shredded cheese. Serve with beans, lettuce, additional salsa and tortillas.