ATLANTIC CITY, N.J. — For a while at least, Miss Vermont was far above the competition to become the next Miss America. A licensed pilot, Erin Connor flew herself from Burlington, Vermont, to an airport just outside Atlantic City on Sunday, three days before the contestants were to meet the public in the annual welcoming ceremony on the famous Boardwalk. “I like to make an entrance anywhere I go,” she said. She completed the 350-mile (563-kilometer) flight in about 2½ hours in a Piper Arrow, with two others aboard.