[Solid]

Flying our flag might serve to highlight the difference between "them and us", and thereby exacerbate existing racial, cultural, social and political tensions.
Flying the US flag may be interpreted as saying- Our Armies Fight For Us.
This isn't the message the coalition forces, IMHO, need to be sending right now. Instead, the differences should be downplayed- Our Armies Fight On Behalf of Us For You.
Our objective, at least in terms of the Iraqi people, was to liberate them from oppression. Of course, it is only natural that we be attempting to achieve other ulterior motives while achieving that former (ie: Democracy in the M.E), but these objectives do not necessarily, obviously, or directly benefit the people. To garner greater support from Iraqi civilians, it seems that we should be down-playing our OTHER "national" objectives, and make it seem like we are working primarily or solely for their objective. Fighting under the US flag emphasises our national objectives, therefore potentially costing us a civilian support base.
At least, this is my take.

I am reminded of the mercenaries that used to fight in Medieval armies. They were fighting for a cause other than their own (the difference being that they were fighting for pay, we for moral reasons [at least partially]). To demonstrate this, they did not fight under the banner of their country or their corps, but instead carried only corps identifiers- patches, livery etc.
By eschewing their national banner, the mercenaries sent the message that their concerns were subsidiary to those of the army for which they fought.

Again, just my opinion.

Thank you,

Solid