Heat 2 tablespoons oil in a large skillet over medium heat. Add sausage; cook and stir until browned, about 10 minutes. Transfer to a plate lined with paper towels using a slotted spoon.
Heat remaining 2 tablespoons oil in the skillet. Add flour; cook, whisking constantly, until dark brown, 8 to 10 minutes. Add chicken, onion, green bell pepper, celery, jalapeno peppers, and paprika; cook and stir until onion softens, 7 to 8 minutes.
Pour chicken mixture into a slow cooker. Stir in cooked sausage, okra, chicken broth, and white wine.
Cover and cook on Low until flavors combine, 7 to 8 hours. Serve over rice.