Stir chicken broth, chicken, potatoes, carrots, and broccoli together in a slow cooker.
Whisk water and quick-mixing flour together in a bowl until a paste-like consistency is reached; stir into slow cooker mixture. Season with salt and pepper.
Cook on Low for 5 hours. Stir baking mix and milk together in a bowl. Drop milk mixture by the teaspoonful into the slow cooker on top of the chicken mixture. Continue cooking, turning the dumplings once, until dumplings are cooked through, about 1 hour more.
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