Turn on a multi-functional pressure cooker (such as Instant Pot) and select Sauté function. Add 1 tablespoon oil, chicken, and sausage to the pot; cook for 6 minutes. Remove meat with a slotted spoon and set aside. Add 1/2 cup oil and flour to the pot. Whisk until roux is the color of peanut butter, about 10 minutes. Add onion, bell pepper, celery, and garlic. Cook, stirring continually to prevent burning, for 5 minutes. Turn the pot off.

Add broth, tomatoes, okra, black pepper, cayenne pepper, thyme, Creole seasoning, and Worcestershire sauce to the pot. Stir in cooked chicken and sausage. Close and lock the lid. Select high pressure according to manufacturer’s instructions and set the timer for 4 minutes. Allow 10 to 15 minutes for pressure to build.

Release pressure carefully using the quick-release method according to manufacturer’s instructions, about 5 minutes. Serve immediately.