It would be risky, but, since the stains are on the white only, a laundry stain remover or mild bleach applied only to the problem area should take the stains out. However, what probably would happen is the treated areas would be lighter and cleaner than the rest of the white. You might try exposing the stained areas only to prolonged sunlight, perhaps dampening them beforehand. I would not have the flag dry cleaned. Practically anything you might try would have some risk, so it might be better to leave well enough alone.