I remember you can change your flag to another country by just putting in your user CP another country's name instead of your own country. But I don't remember ever being able to completely remove them. And I can't honestly suggest that you just switch flags because since I'm a Tommy Haas fan I once changed my flag to a German one in honor of Tommy and people would then post to me in German! And I don't know a word of German!
I'd like such a feature as well. It's not like everybody uses the flag of his nationality anyway. From the technical standpoint it shouldn't be a problem either. If voiding the nationality field isn't doable, just create an option of a grey flag/img of the same colour like the background and name it "none".