Hi there,
This was posted on the other forum (.net) and I thought it was quite interesting and compelling, and it seems to be quite hard to answer for the flat earth activists.
Essentially, on a round earth, the distance from Auckland, New Zealand to Puntas Arenas, Chile by plane is about 6000 miles - a flight time of just over 11 hours, with an airspeed of roughly 530mph.
This image shows a round earth diagram of it:

On a flat earth, the distance would obviously be closer to 30,000 miles, as this diagram shows:

(Thanks to Hob Impost)
Now, Tom Bishop argues a reason for this
To improve your example, you might ask about a non-stop flight from New Zealand to Chile. This would avoid that pesky little stop over that makes the flight look like it takes 7 more hours than it does. If I'm understanding your screenshot, it would take a little over 11 hours to fly from New Zealand to Chile.
Also, check out the Airbus A340 specifications. Check out the "Range fully loaded" value. This plane wouldn't even be able to complete a non-stop flight such as this, on a flat earth. But yet, they're landing in Chile every day. Could this be NASA's handy work?
Now look at cruising speed. FE'ers believe the flat earth has the same diameter as our RE. Which means the circumference of the flat earth is also the same, 24,900 miles. If you put Australia on one side and Chile on the other, the shortest distance should be under 24900 / 2 = 12,450 miles. Now divide that number by the faster of the two cruising speeds, give the FE'er a little benefit of the doubt, and you get a flight time of 12,450 miles / 564 mph = 22 hours, and that's if the plane refuels mid-flight and travels at its cruising speed 100% of the time.
I'm not quite sure I understand his POV, but he later argues that jet streams could allow the plane to reach distances much quicker than thought possible, although since pilots generally might be able to tell by their GPS systems that they were crossing distances hugely quicker than normal...
Anyway, an explanation by some flat earth believers would be much appreciated
Many thanks,
(Thread source:
http://theflatearthsociety.net/forum/index.php?topic=288.0)