Army Regulation 670-1, “Wear and Appearance of Army Uniforms and Insignia,” updated most recently September 5, 2003, addresses explicitly the proper and lawful placement of the U.S. flag patch on the Army uniform.
The regulation states that when authorized for application to the proper uniform the American flag patch is to be worn, right or left shoulder, so that “the star field faces forward, or to the flag’s own right. When worn in this manner, 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’.”
This would give the vision of the flag being led into battle, not retreating, or moving forward.