Make the roux: In a large heavy-bottomed pot, whisk together flour and oil over medium heat. Stir constantly until the mixture turns a deep chocolate brown color, about 15–20 minutes.
Cook the sausage and chicken: Add the sliced sausage and chicken pieces directly to the roux. Cook for 5–6 minutes until lightly browned.
Add vegetables: Stir in diced onion, bell pepper, celery, and minced garlic. Cook for another 5 minutes until softened and aromatic.
Build the broth: Slowly pour in the chicken stock while stirring to combine. Add paprika, cayenne, thyme, bay leaves, and a pinch of salt and pepper. Bring to a boil, then reduce heat and let simmer for 45 minutes, stirring occasionally.
Add okra and shrimp: Stir in the okra and shrimp, cooking for another 10 minutes until the shrimp are pink and fully cooked.
Taste and adjust: Remove bay leaves, taste the gumbo, and adjust seasoning with salt, pepper, or extra cayenne.
Serve: Spoon the gumbo into bowls, add a scoop of white rice in the center, and garnish with chopped parsley and green onions.