I just googled a flight from Johannesburg to Perth, South African Airways have one that last about 9 hours. Some of the other airlines also fly directly from SA to Australia

The really long route according to the Gleeson's New Standard Map of the World (Flat Earth Map) is from Australia to South America (not South Africa). Strangely if you look at flight times for Melbourne on the globe websites you get longer flight times from New York than Buenos Aries.

According to: http://www.travelmath.com

 Melbourne, Australia -> Buenos Aries, Argentina = 14 hours, 57 minutes
 Melbourne, Australia -> Buenos Aries, Argentina = 7,228 miles / 11 633 km
 
 Melbourne, Australia -> New York, USA = 10,359 miles / 16 672 km
 Melbourne, Australia -> New York, USA = 21 hours, 13 minutes
 
The distance of 7,228 miles looks to be accurate according to the Gleeson's flat earth map, yet the value of 10,359 is exagerrated it should probably be no more than 8,000 miles on the Gleeson's flat earth map.

So if that's the case how do they fake a curvature? It looks like what they are doing is going direct according to the flat earth map for the southern hemisphere yet manipulating the northern hemisphere routes to pad the times to portray a curvature.

In other words, a direct flight from New York to Melbourne should really take no more than 14 hours yet they take a long cut and make it take 21 hours.

Gleeson's flat earth map: http://tinyurl.com/ho82otl