Barnabas Webb has been dead for nearly two centuries. But the Revolutionary War soldier—or, at least, the powder horn he used to carry gunpowder—is vexing the world of vexillologists, or flag researchers.

A Virginia innkeeper and history buff claims the engravings decorating Mr. Webb's powder horn, which depict the end of the Siege of Boston in March 1776, contain the earliest known representation of the stars and stripes together on an American flag.

If...