Following is a quote from theDepartment of Defense website...

"Thank you for your inquiry about the proper placement of the American flag on the uniform of the U.S. Armed Forces.

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 flags own right. When worn in this manner, the flag is facing to the observers 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.

We appreciate and share your concern for the respectful display of our American flag on the uniform of the U.S. Armed Forces."