You can book a flight from Buenos Aires, Argentina to Auckland, New Zealand with Air New Zealand non-stop, with a total flight time of 13.36 hours. On Google maps the distance between these two places is about 6400 miles which gives an average speed of 479mph which is what is expected of most commercial airliners.
If the Earth was flat and looked like Azimuthal equidistant 'flat earth' projected map the distance between these two places would be at around 22,000 to 27,000 miles making such a flight impossible in that time.
Please try this for yourself; Air New Zealand numbers are
New Zealand 0800 737 000
Australia 13-2476
USA 1-800 262 1234
Great Britain 0800 028 4149
Eire 1-800 551 447
Canada 1-800 663 5494.
You can also try this with Quantas who fly direct from Sydney and Santiago or Johannesburg, their number from the US is: 1 800 227 4500