What if the United States had been a monarchy instead of a republic? The concept is not completely outlandish. After all monarchy was the default form of government back when the United States seceded from British rule. There was also plans to offer the Prussian prince Henry the throne.
Had the continental congress elected a king the title is not unlikely to have been changed to emperor, once the nation grew westwards.
This is how the flags of such an empire could have looked like.