There were several 13 star flag designs made in the early years of the United States of America. Each star represented one of the original 13 colonies. This 1772 naval flag featured a 3-2-3-2-3 pattern designed by Francis Hopkinson. The Betsy Ross flag featured 13 stars in a circle. More examples can be seen in the more info link below.
Buildings - Flags, Buildings - Indoor
This flag is on display at the Photo Antiquities museum.