Thus, all the symbolism remain meaningless because practically nobody cares about it. And those who care or say so (for whatever purposes) are probably sporting UN emblems, and have been doing that for about half a century.
In reality, if the need arises, we'll use the UN org and its flag to represent Earth, if it's still around (it probably will) and security council can decide upon what to do with the aliens (no idea).
(Assuming the pessimistic but oh-so-realistic scenario, cooperation won't probably work out, so we'll probably have the majority of security council maybe waving the UN flag (if the majority is suitably overwhelming), the others waving whatever alliance symbols they bother to come up with (if at all, in the world wars just different compositions of national flags were popular in the propaganda, and that's not likely to change), and the first global civil war. After it's over and if there's still someone around to declare themselves as the winning side, the victors' flag (which will be used) will be a meaningful flag full of symbolism.)