Heat the oil in a large skillet (one with a fitted lid) over medium-high heat. Add the chicken and cook until golden brown on all sides. Transfer the chicken to a plate (it will finish cooking with the rice).
Add the sausage to the same pan over medium-high heat. Cook until the sausage is golden brown on both sides. Add the sausage to the plate with the chicken.
Reduce the heat to medium and add the butter to the pan. Once the butter has melted, add the flour and stir until blended and smooth. Add the onion, bell pepper, celery, and garlic to the pan and cook for 3 to 5 minutes, until soft.
Add the Cajun seasoning, basil, cayenne pepper. 1/4 teaspoon salt, and 1/4 teaspoon black pepper and stir to coat. Cook for 30 seconds, until fragrant.
Add the chicken broth and diced tomatoes and bring to a high simmer (low boil).
Fold in the rice. Add the reserved chicken and sausage with any accumulated juices on the plate and return to a simmer.
Reduce the heat to low, cover and cook for 20 minutes, until the liquid is mostly absorbed.
Remove the pan from the heat and let stand, covered, for 10 minutes.
Fluff with a fork and let rest for 5 more minutes.
Top with green onions and serve.