I recently purchased a new book with an heraldic theme: Oxford College Arms by John Tepper Marlin. (You can find it on Amazon at a very reasonable price, and I am finding it well worth the reading. It covers the history of the various Colleges and the origin and meaning of their coats of arms.) It does have a few minor issues, in that not all of the blazons of the arms are complete (e.g., in the blazon of the arms of Harris Manchester College, the tincture of the field and the number of torches are missing), but the color illustrations of the arms totally eliminate any questions about what the blazons should be.
But on page 23, in the article on Brasenose College, the author touches on a subject about which I have written before:
[M]any (including the author) believe that the mullets and bars of the Washington arms were a decisive influence on the creation of the U.S. Stars and Stripes.
For my earlier take on this topic, and Dr. Marlin's responses to it, you can find my October 8, 2012 post, "An Old Controversy Refuses to Die" at https://blog.appletonstudios.com/2012/10/an-old-controversy-refuses-to-die.html
The flag of the United States of America was officially described in a Flag Resolution passed by the Second Continental Congress on June 14, 1777:
Resolved, that the flag of the thirteen United States be thirteen stripes, alternate red and white; that the union be thirteen stars, white in a blue field, representing a new constellation.
The most recent iteration of that flag, with fifty stars for each of the fifty states, is shown here.
The question is how much, if at all, did the Washington coat of arms (below, from an old postcard) influence the design of that flag.
My argument is that the Washington arms had no influence upon the design of the US flag at all, and that the US flag was a simple evolution from a series of flags, generally naval, that logically resulted in the flag codified by the Flag Resolution of 1777.
Thus we move in progression from the flag of the East India Company used from 1600 to 1707:
To the flag of the East India Company used following the union of the crowns of England and Scotland, used from 1707 to 1801: