A New Zealander (on IS) was saying that the Ashes should be kept in NZ since Stokes was from that country! I've no idea if there is any basis for that!
Sure he was born in NZ, but came to England when he was 12, so pretty legitimately English as he's played all his career here. He isn't one of these players who qualified by residency as a professional.
And no they can't have the ashes - only England or Australia can.