Combine the peaches, sugar, flour, cinnamon, nutmeg, and allspice in a 4-quart Dutch oven. Allow the mixture to sit until the dry ingredients are dissolved and a syrup forms, about 15 minutes. Bring the peach mixture to a boil over medium heat. Decrease the heat to low and cook until the peaches are tender, about 10 minutes. Remove the mixture from the heat and add the butter.