Turn the Instant Pot onto Sauté and add the butter or oil and flour to the Instant Pot. Whisk together until butter melts and the two combine. Cook for no more than a minute more.
Add the chicken broth and the seasonings. Whisk everything together and continue to stir until the gravy begins to simmer. Let it simmer for about 1 minute. Then turn the Instant Pot off.
Carefully, place the chicken in the Instant Pot and make sure to spoon some gravy over the top to be sure it is coated.
Use the slow cook function, adjust it to the low setting, and cook for about 4-5 hours (exact time will depend on how thick your chicken breasts are). Check your chicken at 4 hours to avoid drying it out.
Shred the chicken up in the gravy, and serve over mashed potatoes with your favorite sides!