Hi there,
I think you'll find that BA does not fly the Pacific route to NZ---they go via the far East.You can certainly fly BA to the west coast of USA but then would have to find out if a partner airline in the OneWorld alliance flew to NZ via the Pacific islands.Air NZ seems to have the monopoly on island stopovers and they are with Star Alliance.American Airlines might fly in to NZ but don't know if they do island stops.Going this route it's about 12 hours UK--LA then about the same again to Auckland.Other OneWorld partners are Quantas and Cathay Pacific--both flying the eastern route.