That's actually super simple.
Tahiti: 17.6509° S, 149.4260° W
Punta Arenas: 53.1638° S, 70.9171° W
These are reference points in relation to the north pole, a point that is the same on both the globe and flat Earth. Distances from the north pole are not under contention by either globe Earth or flat Earth proponents. Each degree of latitude is approximately 69 miles apart.
Now enters the math.
Tahiti is 107.6509° south of the north pole, times 69 miles per degree = 7428 miles away from the north pole.
Punta Arenas is 143.1638° south of the north pole, times 69 miles per degree = 9878 miles away from the north pole.
They are 78.5° apart.
With 3 known parts of a triangle, we can use trigonometry, or in your case a triangle calculator like found here:
http://www.calculator.net/triangle-calculator.htmlSo we can enter our known values, values which are undeniable, regardless of the shape of the Earth, and find out how far apart the two points on the map are.
If the Earth is flat, the two points MUST be 11,112 miles apart. Because math.
If the Earth is not flat, the calculation is useless for application over a globular surface.
You obviously contend that the flight you quoted was made. It was made by an aircraft with a normal operating range of 1,250 miles (on a 90 gallon fuel tank), that was modified to carry 361 gallons of fuel. Disregarding the fact that the weight of the extra fuel would at least somewhat shorten the range of the aircraft, and instead giving you every benefit of the doubt, we can say that the modified aircraft has a range 4 times the unmodified one (361/90 = ~4). 4x the range of 1,250 miles = 5,000 mile range. Again because math. So what we have is a flight you yourself have admitted occurred, by an aircraft that doesn't have the range to make that flight IF THE EARTH IS FLAT AS YOU CONTEND.
This is a purely mathematical refutation that the Earth is flat, by data points that are not in contention by you. In the field of logic, we have what is known as reductio ad absurdum. It is impossible. Flat Earth is disproven.
You failed, as predicted.
Distances and directions from all places are true only from the center point of projection (North Pole). Distances are correct between points along straight lines through the center. All other distances are incorrect.
Distortion of shapes and areas increases with distance from the center point.
Longitudinal lines are equal distant from center point. Latitudinal lines are NOT equal distant from the center point. But the Equator is equal distance to the Longitudinal lines.
This video helps explain why the Gleason's Map is correct and how you made your mathematical errors.