Thinly pound the chicken, then sprinkle both sides with salt and pepper. Place the flour in a shallow dish.
Add the oil to a pan set over medium-high heat. Dredge the chicken in the flour, then shake off any excess. Cook the chicken until browned, 3 to 4 minutes on each side. Remove from the pan and set aside. Reduce the heat to medium, add the prosciutto, and saute for 1 minute. Add the mushrooms and cook until soft, 5 minutes. Add the marsala and cook to reduce, a few seconds. Add the stock and bring to a simmer. Stir in the butter, then return the chicken to the pan and simmer for 1 minute. Season with salt and pepper, and garnish with the chopped parsley to serve.