Three weeks after Hurricane Gilbert destroyed Jamaican homes and businesses, relief supplies for the island are piled up in churches and armories across New York because of a bureaucratic snafu, frustrated relief workers said. More than 300,000 pounds of medicine, food, building materials and clothing are sitting in facilities from New York City to Buffalo because the federal government will not allow the state’s National Guard to take them to Jamaica. Federal authorities want commercial airlines to carry the supplies to the island, but those airlines do not have the space to handle the material in a timely fashion, said Dr. Waldaba Stewart, chairman of the Caribbean Action Lobby. Gov. Mario M. Cuomo offered to have the state’s National Guard fly one of its C-130 cargo planes to Jamaica with the supplies at no cost to the charitable groups. But a federal law known as the Economies Act requires that even charitable goods fly commercially, officials said.