You need either A) have the KrisFlyer number entered into the booking, or B) access via a webform to provide your KrisFlyer credentials once airborne and wifi is active.

A. I flew on SQ metal under a NZ codeshare, and needed the SQ Lounge staff to add my KrisFlyer ff number into the booking (specifically FQTS) whilst retaining my NZ Airpoints ff number as the mileage earning number (in FQTV). Lounge staff were well practised and didn’t my detailed information… 😀

B. An alternative is that it is possible to gain wifi access by providing your KrisFlyer credentials on a webform once airborne and there is limited local wifi available to do this. It worked well despite a number of additional steps