I find NZ very inconsistent regarding ability to cancel flexi bookings in app/online. I find ~50% of the time processing the cancellation in app/online works as expected and the other ~50% it does not work and refers me to the 0800 number. I suspect it's not entirely a booking channel issue, since I've had this issue several times on tickets I have personally booked via the NZ website directly (I never use an agent etc). One issue I know of is that if you are already checked in, then you are required to phone in so the phone agent can find a supervisor to manually offload you and then process the cancellation--fustrating if you check in the day before and on the day of travel it turns out you do not need to (or can't) travel. Took me two and a half hours on the phone (including 25mins on hold just for the offload to be done) to them to sort out a cancellation I had recently (pre-flooding). I can't imagine how bad the phone queues must be now all because their own app/website does not make this easy. Interestingly enough I've had much better success with canelling flights online with JQ (including one where I had checked in and their website was able to offload me and process the cancellation) with only one cancellation I've had to contact JQ to sort out manually.
Self-service has never been a strength of NZ but they really need to improve this.
Thank you
gratn for the idea to simply change your flghts and deal with the cancellation later when the call centre is quieter. Will try that next time.