In 3- to 4-quart slow cooker, mix chicken, carrots, mushrooms, onion, water, garlic powder, thyme and broth.
Cover; cook on Low heat setting 7 to 9 hours.
About 35 minutes before serving, skim fat from slow cooker. In small bowl, beat soup, milk and flour with wire whisk until smooth. Add soup mixture and broccoli to chicken mixture. Cover; cook on Low heat setting 30 minutes longer or until broccoli is tender.