On the Army's current desert-camo uniform and woodland-camo battle-dress uniform, a full-color flag is worn on the wearer's right sleeve -- basically "backward" so that the union (the blue field with the stars) is to the wearer's front. (It's "backward" because the normal flag protocol is to display the flag with the union to the flag's own right/the observer's left.)
If the soldier is authorized a "shoulder sleeve insignia, former wartime service" -- commonly called a "combat patch" -- for the right sleeve, the U.S. flag is worn under the combat patch on the DCU and BDU.
In the pics of and information I've seen about the new Army combat uniform, the flag is on the right sleeve with the union forward but is worn above the combat patch.
To cloud the issue, there are some units wearing field-test versions of the new uniform in the current three-color desert-camo scheme, and some are wearing the flag on the left sleeve, and some wear a subdued flag.
Basically, though, it's full-color on the right sleeve with the stars to the front.
HopeRegards,
Chris
Baghdad