We appreciate and share your concern for the respectful display of our American flag on the uniform of the U.S. armed forces. While each service branch has its own uniform regulation, please see the Department of the Army Regulation 670-1 Pamphlet: Guide to the Wear and Appearance of Army Uniforms and Insignia: https://armypubs.army.mil/epubs/DR_pubs/DR_a/pdf/web/ARN6028_DAPam670-1_Web_FINAL.pdf.
Chapter 19 addresses this issue specifically. It states, in part, "The U.S. flag embroidered insignia is worn so that the star field faces forward, or to the flag's own right. When worn in this manner, the flag is facing the observer's right and gives the effect of the flag flying in the breeze as the wearer moves forward."