This is what the US Flag Code states. Hope it helps !
Q6: How should the American Flag patch be worn?
The U.S. Code states "no part of the flag should ever be used as a costume or athletic uniform. However, a flag patch may be affixed to the uniform of military personnel, firemen, policemen, and members of patriotic organizations. The flag represents a living country and is itself considered a living thing. Therefore, the lapel flag pin being a replica should be worn on the left lapel near the heart."
The U.S. Code does not address the positioning of the flag patch. It is appropriate to wear an American flag patch on the left or right sleeve. When worn on the left sleeve, the union would appear towards the front and the stripes would run horizontally toward the back. When worn on the right sleeve, it is considered proper to reverse the design so that the union is at the observer's right to suggest that the flag is flying in the breeze as the wearer moves forward.
Since the law does not specifically address the positioning of the patch, a decision is left to the discretion of the organization prescribing the wear. As many states and cities have ordinances pertaining to the use of the flag, you may wish to contact the Attorney General of your state or the City Attorney's office regarding this matter.