Cook the andouille and kielbasa in a large nonstick skillet over medium heat until browned, about 8 minutes. Remove the sausages from the skillet and drain on paper towels.
Heat the oil in a large Dutch oven over medium-high heat. Gradually whisk in the flour and cook, whisking constantly, until the flour is a deep caramel color, 7 to 10 minutes. Reduce the heat to medium and stir in the celery, onions, bell peppers, garlic, Creole seasoning, thyme and cayenne. Cook for 5 minutes, stirring constantly. Gradually stir in the broth, then add the tomatoes, okra, Worcestershire and sausages.
Increase the heat to medium high and bring the mixture to a boil. Reduce the heat to low and simmer, stirring occasionally, for 20 minutes. Stir in the shredded chicken and allow it to warm in the gumbo for 2 to 3 minutes.
Serve the gumbo over hot cooked rice, topped with scallions. Serve with hot sauce, if desired.