The jackstaff was out on the bowsprit, at the very front of the ship. The striped rattlesnake flag is called the "first navy jack", but the jack was not flown while the ship was under way. It got in the way of the foremast stays (after the method of rigging was changed in the 1720s), so it was only flown while the ship was in port. Commodore Hopkins' descriptions of the snake flag indicate that it was used as his command flag, and not as a jack.
Thanks for the education.