In a large, deep skillet or Dutch oven, heat the vegetable oil over medium heat. Once hot, add the flour and whisk continuously to make a roux. Cook until the roux is a deep brown color, about 10-15 minutes.
Add the diced onion, bell pepper, and celery to the roux. Cook until the vegetables are soft, about 5-7 minutes.
Stir in the garlic, andouille sausage, and chicken thighs. Cook until the sausage is browned and the chicken is no longer pink, about 8-10 minutes.
Pour in the diced tomatoes with their juices, and add the bay leaves, Cajun seasoning, thyme, smoked paprika, salt, and pepper. Stir well to combine.
Gradually add the chicken broth, stirring constantly to prevent lumps. Bring the mixture to a boil, then reduce the heat and let it simmer for about 30 minutes, stirring occasionally.
Add the shrimp and okra to the pot. Cook until the shrimp are pink and opaque, about 5-7 minutes.
Remove the bay leaves and ladle the gumbo over cooked white rice. Garnish with chopped parsley and sliced green onions. Serve hot and enjoy!