Combine flour, salt, and pepper in a shallow dish. Coat chicken pieces with flour mixture. Brown chicken in hot oil in a 4- or 5-quart Dutch oven, turning once. Remove chicken.
Add onions and garlic to pan and cook until tender. Add basil or other dried herb and red pepper; cook and stir 1 minute more. Carefully stir in broth and undrained tomatoes. Add browned chicken, green beans, and carrots; bring to boiling. Reduce heat, cover, and simmer for 15 minutes. Stir in potatoes; cover and simmer 20 minutes more or until vegetables and chicken are tender. Makes 4 to 6 servings.