Heat 1 Tbsp. oil in a Dutch oven at medium heat. Add in Andouille sausage and chicken, cook until they being to brown, about 5 minutes. Set aside.
Clean out Dutch oven and heat remaining oil over medium heat, gradually whisking in flour. Keep whisking and cook until mixture starts to darken, about 10 minutes.
Stir in onions, green pepper, celery and garlic. Cook, stirring frequently, until they start to get tender, about 15 minutes. Stir in thyme, black pepper and red pepper.
Add vegetable broth and bring to a boil. Reduce to a simmer, stirring occasionally. Cook for 1 hour. Add sausage and chicken back in and cook for another 5 minutes.
Remove from heat and serve over cooked rice and with green onion garnish.