Bring 2 cups lightly salted water to a boil in a covered 2 quart saucepan. Add the rice, stir, and reduce heat to low. Cover the pan and simmer until rice is tender.
Meanwhile, melt the butter in a 4 1/2 quart Dutch oven or soup pot over medium heat. Finely chop the onion and add them to the pot. Cut the chicken into bite sized pieces and add to the pot. Raise heat to medium-high. Cook, stirring, until the chicken is almost cooked through, about 4 minutes.
Meanwhile, cut the sausage link in half lengthwise. Slice both halves into roughly 1/4 inch pieces. Add the sausage to the pot and continue to cook, stirring from time to time, while you stem, seed, and cut the bell pepper into bite-sized pieces. Add the broth to the pot, raise the heat to high, and add the bell pepper. Cover the pot and bring the soup to a boil. Add the Cajun seasoning. Re-cover the pot, reduce the heat to medium, and cook at a moderate boil until the bell pepper is tender about 3 minutes.
In a small jar, mix the flour with 3 tablespoons of cold water until there is no lumps. Gradually add the flour mixture to the soup stirring constantly until thick. Serve with rice.