Not always. The American Army's flag patch on the right shoulder is on the upper right. There was a big discussion at www.americasarmy.com in the forums.
THe federal directive says it is that way so it looks like a flag waving in the wind as the soldier moves forawrd. If the flag had the stars in the upper left it would look like he is retreating.
Noted..I was always taught they go in the upper left..