Tom, from what I read in discussions, you said GPS and other means of calculating distance is based on Round Earth. What OP is trying to say is that these(GPS and others) work even though they are based on Round Earth model.
A plane may use a GPS device to get to the destination, but there is no verification that the plane traveled exactly the distance listed. The coordinates take you to real places if you attempt to follow them. The distance between the coordinate points are computed based on a globe, however.
There is no real independent test of the distances, either, since planes do not have odometers. Airspeed measuring devices are measuring fluids moving within fluids and are not reliable or used in navigation. They are only used for determining the speed of air over the wing for when making banking maneuvers and such.
However, Flat Earth model does not even have a proper map!
How are we supposed to make a map when the distances planes fly are all based on a round earth coordinate system?
The problem with creating a map and model is that those listed distances found on the internet rely on a Round Earth coordinate system to compute a distance. No one has ever verified the accuracy of the distances computed from that coordinate system. No one has ever taken a tape measurer across the Atlantic to verify the spherical lat/lon distances, for example.
If we accept the round earth coordinate system as true, we might as well accept that the earth is round. The claim that GPS, or whatever Round Earth coordinate device, is true and accurate, is a positive claim brought to these discussions which must be demonstrated as accurate.
From our everyday experience, we know that Round Earth model work(ex-driving using navigation). You just cannot say Round Earth model is wrong and Flat Earth model is right without any actual model.
Simple navigation by setting a heading for a coordinate point is not enough. It is possible to travel the world with a Mercator map where Greenland is larger than Africa and Antarctica is larger than all of the continents combined. There needs to be verification of distances for the navigation to have meaning in regards to the form of the world.