Their claim is they can no longer live in their country. They decide to wave a patriotic flag. What's your advice?
1) Wave no flag at all...you are supposed to be country-less.
2) Wave the flag of the country from which you are seeking asylum. You want them to feel good about you, and less likely to turn you around.
3) Wave the flag of the country which persecuted you or declines to protect you. Make it look like a mini-invasion...wave the invading country's flag while you tear down the receiving country's border fence.
I would go with option 1. Why are they even waving a fucking flag? Most people around the world think it is weird for private citizens to be fly national flags. Option 3 is not defensible advice.