QF 321 is a code share on LA800. LA is going through a minor crisis because their 787s are not flying. Aircraft are operated in odd and unpredictable ways. One week ago the Friday QF321 SYD-AKL was cancelled and the same happened again this Friday. Indeed it operated AKL-SCL but 4 hrs late. It started the outbound journey 14 hrs late from SCL. As a QF code share, e QF staff can't really help with anything on LA but do their best with shuffling you around on QF metal.

So, the survival kit.

Check flight status from at least 26 hrs prior. This was when I saw the cancellation on the QF web site.
If cancelled, get on the phone ASAP to secure a suitable seat on an alternate flight. Everything zeros out very quickly. Chatting with someone else, they said that QF rang to advise of the cancellation 12 hrs after I got on the phone. In other words, don't wait to be contacted - do it yourself.
The new flight(s) to get you to AKL so you can join the LA flight may be via MEL (sigh). If via MEL, you can negotiate on the timing of the SYD-MEL connector.
Expect to be rejected if you dare to suggest that you could be rebooked on EK or NZ.
If routed via MEL and doing GST refund before MEL-AKL, allow a 2'hr connection (and at least 30 min in the GST refund queue)
If you arrive in AKL without a AKL-SCL Boarding Pass, the Transfer counter will gladly help - so long as the LAN rep can be found to unlock the LA system so a BP can be issued. Expect to wait more than half an hour.
The transfer counter staff will give out $15 meal vouchers and a $10 duty free voucher to keep you happy during the delay to boarding in AKL. But only if you can show a boarding pass. Too bad if "Mr LAN" can't be found to open up their computer...
If you had seat assignments, you would have remembered that on LAN flights these are aspiration all rather than truth. Seat allocations seem to disappear at T-24 hrs. Upon BP issuance, if 2 or more travelling together you will probably by now be separated (given its now only 1 hr prior to departure). The desk clerk will move people so you can sit with your travelling companion if the clerk likes you.
By now it's boarding time and you enter another world when on the plane. Calm, friendly, attractive, welcoming, efficient, comfortably flat beds (in Biz) and everything you could ask for. All this for flying on a QF code share

I'd hope LA schedules recover when their 787 get in the air again.

But after all this, using the QF code gets an extra 5000 or so FF points and a ~.