Is there a reason why New Zealanders, despite being Commonwealth and British derived, sound more like Americans than the Australians who are next door?
The "british" accent as we think of it has evolved greatly since the colonial era. I'm not a linguist but I'd suggest the similarities you hear between Kiwi and American accents are things that were ubiquitous at one time then other English speakers lost them along way.
Because American English and New Zealand (and Australia) all derived from British English, obviously, but have drifted less than the accents in Britain. US, NZ, and AUS all drifted differently but the three may still be closer to the British English from the time their colonies were established.