Wincing Devil.
I was also surprised by the flag, I thought there were too many stripes, but checked and you're right on that, but there should be 15 stars.
On June 14, 1777, in order to establish an official flag for the new nation, the Continental Congress passed the first Flag Act: "Resolved, That the flag of the United States be made of thirteen stripes, alternate red and white; that the union be thirteen stars, white in a blue field, representing a new Constellation."
Act of January 13, 1794 - provided for 15 stripes and 15 stars after May 1795.
Being Welsh, I had to check first, but found the info Here