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Big Flats Fire Department Protecting the Citizens of the Town of Big Flats PHONE EmergenciesCall 911 For nonemergencies call the fire station at 6075623063 505 Maple Street Big Flats NY 14814 The Town of Big Flats is located on the western border of Chemung County in the Southern Tier region of New York State. It is roughly midway between the cities of Corning and Elmira. It is comprised of a bit more than 46 square miles and Big Flats Volunteer Fire Department serves more than half of the Town. The balance is served by three other volunteer fire departments.