Why are the American flag patches on the right shoulder of current
military uniforms backwards?

Dear wabcoll-ga,
According to this article in the CML Army Chemical Review, Oct, 2004, 
by Lisa Burgess (and the European edition of Stars and Stripes),

"The Army has two authorized flag patches, one to be worn on the left
shoulder, with the canton on the left. and another "reverse field"
patch worn on the right shoulder, with the canton on the right. The
two different orientations are mandated because Army regulations call
for the flag ?to be worn so that to observers, it looks as if the flag
is flying against a breeze? [...] So if a soldier were charging into
battle, the flag would give the appearance of forward motion."

Further information appears here
http://www.findarticles.com/p/articles/mi_m0IUN/is_2004_Oct/ai_n7069358

I hope this answers your question. If it does not, or the answer is
unclear, then please ask for clarification of this research before
rating the answer. I shall respond to the clarification request as
soon as I receive it.
Thank you
answerfinder

Search strategy
"flag patches"  "right shoulder" led me to references to the above
article which I found by "Is the Flag 'Backwards' on Soldiers'
Sleeves?"
://www.google.co.uk/search?q=%22Is+the+Flag+%27Backwards%27+on+Soldiers%27+Sleeves%3F%22&hl=en&lr=&start=10&sa=N

Answerfinder-ga provided a very good answer to your question, but let
me also add this:

What is the importance of the appearance of forward motion?

If the "backward" flag were reversed the direction of forward motion
would also be reversed. In effect, it would give the appearance of
retreat - an unfathomable subject to the US military.

GOOGLE:
://www.google.com/search?hl=en&q=flag+patch+backward

"A flag bearer rushing into the fray, then, would naturally lead with
the stars. In fact, it would be virtually impossible to lead with the
stripes?the flag would simply wilt and wrap around the pole, rather
than waving triumphantly in the wind."

MSN
http://slate.msn.com/?id=2080338

You will note that this same practice is observed on the tail of all
military aircraft including the President's personal airplane, Air
Force One.

http://wallpaper.net.au/wallpaper/aviation/Air%20Force%20One%20-%201024x768.jpg


Tutuzdad-ga

I would add to the comment of tutuzdad-ga that a retreat is
unfathomable to not just the United States military but any military
in history.

Well, except for the French.  Cheese eating surrender monkeys!

Touché oheric.  But first, they draw their stronger allies into the
maelstrom.

Dear wabcoll-ga,
Many thanks for your tip. Pleased I could help.
answerfinder-ga