No, the "official" Ohio flag is not a rectangular shape.. it's defined more as a swallow-tail pendant, which is what I think he's referring to? He wants the flag to be the actual shape.
And
@DieselMinded, odds are even if you do get it in that shape (which you can easily do with using PhotoShop and giving transparent background to the areas that are currently white) you will still have to have some color background (other than white) to display behind it. I really don't think you will easily be able to get it to display in it's native format like what I think you are asking for. Even if using CSS, it's probably going to be rather complicated - even if it can be done.