In a large skillet, heat olive oil over medium-high heat. Add chicken pieces and cook until lightly browned, about 4-5 minutes. Remove chicken and set aside.
In the same skillet, add sliced turkey sausage and cook until browned, about 3-4 minutes. Remove and set aside with the chicken.
Add diced onion, green bell pepper, and celery to the skillet. Cook until softened, about 5 minutes. Add minced garlic and cook for 1 more minute. Remove vegetables and set aside.
In the same skillet, whisk together vegetable oil and all-purpose flour over medium heat to make a roux. Stir constantly for about 5-7 minutes until the roux is medium brown and fragrant. Be careful not to burn it.
Transfer the roux to the slow cooker. Add the cooked chicken, sausage, sautéed vegetables, chicken broth, diced tomatoes with juice, Creole seasoning, dried thyme, bay leaves, smoked paprika, and cayenne pepper. Stir to combine.
Cover and cook on low for 6 hours.
About 30 minutes before serving, stir in sliced okra. Continue cooking with the lid on.
Remove bay leaves. Taste and season with salt and black pepper as needed.
Stir in chopped parsley and sliced green onions just before serving.
Serve the gumbo hot over cooked white rice.