Heat oil in 12” skillet over medium-high heat. Add sausage and ham. Cook until golden brown on all sides, about 3 minutes. Transfer sausage and ham to plate. Add peppers, onions, celery, garlic, chili powder and hot pepper flakes to same skillet. Cook, stirring occasionally, until onions are soft and translucent, about 5 minutes more.
Stir shrimp, tomato sauce and reserved sausage and ham into skillet until combined. Add contents of yellow rice packet mix and 2 cups water to skillet; stir to combine. Bring liquid to boil. Reduce heat to medium low. Simmer; covered, until rice is tender and water is absorbed, about 25 minutes.
Remove skillet from heat. Gently stir jambalaya to combine. Serve warm.