The milk used to cook mashed potatoes is usually just added for flavor of the mashed potatoes and you can easily cook mashed potatoes with just plain water if you're allergic to milk or don't have any milk.
If you want to add some flavor to your mashed potatoes though you can use chicken broth and cream or vegetable broth or soy milk or even some sour cream to give the mash potatoes a good flavor without milk.