The website mentions silk organza at https://1worldflag.com/flag/. That's where my mind went initially, some kind of sheer silk fabric. I don't know how durable it would be in the elements though.
You could make any flag out of non-vegan materials, sure. But that this flag was designed with the basis of cruelty (silk) makes it also conceptually non-vegan.
What a great way to unite the world in a practice of cruelty to its inhabitants