Planes navigating an 'actually flat Earth' by 'incorrect round Earth coordinates' would then appear to have significantly worse fuel efficiency and travel much slower in the Southern hemisphere.
Flying ~3650 miles from New York to Paris takes x amount of fuel... flying (what the pilots, Tom claims, erroneously think is) ~3750 miles from Rio de Janeiro to Cape Town takes 3x, 4x, 5x... some much greater amount of fuel. It would take the same proportion of time longer.
This is not the case. Ergo, the flat Earth model fails to correctly predict distances in the Southern hemisphere.