Girl With The American Flag

On U.S. military uniforms, flag patches are worn on the right shoulder, following the vehicle convention with the union toward the front. This rule dates back to the Army's early history, when both mounted cavalry and infantry units would designate a standard bearer, who carried the Colors into battle. As he charged, his forward motion caused the flag to stream back. Since the Stars and Stripes are mounted with the canton closest to the pole, that section stayed to the right, while the stripes flew to the left.
Other organizations that wear flag patches on their uniforms can have the flag facing in either direction. The uniform of the Boy Scouts of America, for example, has the stripes facing front, the reverse of the military style. Law enforcement officers often wear a small flag patch, either on a shoulder, or above a shirt pocket.
Every US astronaut since the crew of Gemini 4 has worn the flag on the left shoulder of his or her space suit, with the exception of the crew of Apollo 1, whose flags were worn on the right shoulder. In this case, the streaming convention (canton on the right) was not observed.