Any type of chicken will work for this recipe, including rotisserie chicken, but you won't need to slow cook it if you use fully cooked chicken. You will just need to warm up the soup.
The Instant Pot is not my preferred method to use for this recipe. Potatoes pressure cook faster than chicken. So in order to cook them at the same time, you will need to cook the chicken for 3 minutes, 10 minutes is my preferred time for really juicy chicken. The chicken is fully cooked at 3 minutes, but you may find that it isn't super tender.