Upvote:6
Yes, you can book your ticket with the New Zealand passport and use the Taiwan passport to enter the US. You could also book the ticket with the Taiwan passport and use the Taiwan passport to enter the US, which is likely to be simpler, as the airline won't get confused by your having two passports (I've never known an airline to be confused by that, but it's possible).
Also, because New Zealand is a member of the "six month club," you can use the New Zealand passport to enter the US even within six months of its expiration, as long as you will leave the US before it expires.
(Taiwan is also a member of the six-month club.)