Damn AI interpreters! OK, I'd better explain myself then:
Правилами разрешено носить патч в виде флага на правом рукаве униформы только в том случае, если поле со звездами направлено в сторону переда (передней части) туловища солдата. Делается это потому, что флаг не должен представлять вид "знамени отступающих", а именно так он выглядит в случае, если поле со звездами направлено "от" боя.

Вот более подробное объяснение.
U.S. Flag Reversed Patch 2" X 3 3/8" with Yellow Border
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.
Wear of full-color U.S. flag cloth replica:
a. General. All soldiers throughout the Force, regardless of deployment status, will wear the full-color U.S. flag cloth replica on utility and organizational uniforms.
b. Description. The colors of the U.S. flag cloth replica are red, white, and blue. The size is approximately 2 inches by 3 inches.
c. How worn.
When approved for wear, the full-color U.S. flag cloth replica is sewn 1/2 inch below the right shoulder seam of the temperate, hot-weather, enhanced hot-weather, and desert BDU; the BDU field jacket; and the cold-weather uniform. If the SSI–FWTS is worn on the right shoulder of the utility uniform, the full-color U.S. flag cloth replica is placed 1/8 inch below the right shoulder sleeve insignia. The SSI–FWTS is not authorized for wear on organizational uniforms, unless indicated above.

The full-color U.S. flag cloth replica 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 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.

Основные моменты выделил подчеркиванием.

PS: Японцы, видать, тоже были не в курсе, поэтому когда шили реплику броника, патч нагрудный тоже сделали зеркальным (см. мой аватар). Прийдется заказывать отдельно.