Do you know if anyone has done some kind of National Flag of Westeros? And if not do you have any idea what something like that would look like?

I don’t think there is one. There isn’t really a conception of the nation apart from the monarch themself – so for three hundred years, it was the Targaryen dragon. For 15-odd years, it was the Baratheon stag, but now that symbol’s been fractured between no less than three different groups.