Place chicken breasts on a cutting board and cover with plastic wrap. Use the flat side of a meat tenderizer to flatten the chicken breasts evenly to about 1/2-inch thickness.
Place flattened chicken breasts in a zip-top bag with flour, salt, and pepper. Shake to coat chicken with flour mixture.
Heat Instant Pot to Saute and add oil. When hot, add chicken and cook for about 4 minutes on each side until golden brown. You may need to do it in batches. Remove chicken to a plate.
Add prosciutto and mushrooms to Instant Pot and cook until prosciutto is crispy and mushrooms are browned. Add Marsala wine and chicken stock and scrape the brown bits off the bottom of the pan.
Add the chicken back in and settle it down into the liquid.
Put cover on (make sure vent is turned to “seal”). Set Instant Pot to Manual (high pressure) for 10 minutes.
Once done, quick release the pressure. Use an instant read thermometer and ensure chicken has an internal temperature of 165 degrees Fahrenheit.
Stir butter into sauce until melted.
Serve chicken topped with mushrooms, sauce in pan, and fresh parsley.