I get asked quite often why the flag is backward, the short answer is... it's not. The flag should always be displayed in the direction of travel or appear as if it is blowing in the wind.
According to the Department of Defense website, Army Regulation 670-1, “Wear and Appearance of Army Uniforms and Insignia,” tells us the proper and lawful placement of the U.S. flag patch on the Army uniform. The regulation says when applied properly to a uniform the American flag patch is to be worn, right or left shoulder, so that “the star field faces forward.
So a left shoulder patch looks "normal" or as expected, however, if you are looking at a patch on the right shoulder, the flag is facing to the observer’s right and gives the effect of the flag flying in the breeze as the wearer moves forward. The appropriate replica for the right shoulder sleeve is identified as the ‘reverse side flag’.