Make the roux: Heat 2 cups vegetable oil in a large Dutch oven over medium-high heat until hot, about 5 minutes. Reduce the heat to medium, then whisk in the flour in 2 additions until the mixture is the consistency of cake batter. Continue cooking, whisking constantly, until the roux is dark brown, about 20 minutes. Remove from the heat, then stir in half each of the onion and bell peppers. Set aside until ready to use.
Combine the whole chicken, 10 cups water, the red pepper flakes, 1 tablespoon salt and 1 teaspoon pepper in a large pot. Bring to a boil and cook 1 hour. Strain the broth, then return to the pot and set aside. Remove the chicken skin and bones, then cut the meat into bite-size pieces.
Heat the remaining 2 tablespoons vegetable oil in a medium skillet over medium heat. Add the chicken sausage and cook, turning, until cooked through, 6 to 8 minutes. Let cool slightly, then slice.
Add 16 cups water to the pot with the broth and bring to a boil. Add the roux; cook over medium-high heat, stirring, until it dissolves, about 5 minutes. Stir in the remaining onion and bell peppers. Return to a boil, then reduce the heat to medium, cover and cook, 1 hour. Add the andouille sausage and raw chicken breasts, reduce the heat to medium low and cook, covered, 30 more minutes. Add the smoked turkey, sliced chicken sausage, cooked chicken pieces and scallions and simmer, covered, 30 minutes. Skim the fat off the surface, then stir in the Cajun seasoning. Serve over rice.