The question is, of course, how can you account for the fact that known airplane flight times follow the can be accurately predicted with an assumption of a spherical earth and cannot be with a flat earth?
You cannot use flight times to conclude that the earth is any shape. Flight times cannot be accurately attributed to any distance or journey. There are dozens of reasons why an aircraft will take the amount of time it does to make a journey.
The first reason is that you never fly direct to your destination.
1) You will always take off and land into wind. This means you may fly in the opposite direction to your intended travel on take off and then having gained enough altitude to be clear of the airport and usually city below, make a turn onto the SID (Mentioned below).
2) Landing is the same. You may have to fly past the airport round the back of it to approach the active runway using a STAR.
3) You must follow a SID when you leave an Airport and use a STAR when you approach one. These take you all over the place to avoid overflying cities for noise abaitment and for terrain clearance on take off and to position aircraft for traffic controllers to feed them in for final approach at the right times for landing. You are also tracking over beacons that are laid out in fields in the middle of nowhere.
http://en.wikipedia.org/wiki/Standard_Instrument_Departurehttp://en.wikipedia.org/wiki/Standard_Terminal_Arrival_Route4) You may well be placed in a hold. 4 minute race tracks in a stack. You join at the top and aircraft will be stacked every 1000 feet all the way down. When the controller wants another aircraft, he takes one from the bottom. You will not be able to factor in traffic density into your calculation, so cannot say how long you might hold for. You might not hold at all.
http://en.wikipedia.org/wiki/Holding_(aviation)
5) Most routing, especially in remote places is going to be using routes that rely on beacons such as VOR's or NDB's. Following these again takes you out of your way.
6) When crossing oceans you will be forced by law to use a track system for aircraft separation. These change daily due to the weather and again traffic. You can't ever say which route you used on your flight as a passenger.
http://en.wikipedia.org/wiki/North_Atlantic_TracksAircraft performance is another major factor
1) You cannot say how much your aircraft weighed on that day. This effects climb performance and cruise. Altitude effects speed.
2) As altitude effects speed you would need to know how high you flew that day. The higher the quicker, due to the widening difference in IAS and TAS.
3) Even the same aircraft types may have different engines. This again effects performance calcs for climb.
4) Temperature plays a large part. Warm air ruins performance. You need to know how hot it was. Temperature also effects Mach number. Commercial aircraft don't fly speeds, they fly on a mach number. As the local speed of sound will vary from day to day you can never be sure how fast you are actually flying.
http://en.wikipedia.org/wiki/Mach_numberhttp://en.wikipedia.org/wiki/Critical_Mach_number5) Atmospheric pressure effects performance. A high pressure is going to hamper your climb out.
http://www.experimentalaircraft.info/flight-planning/aircraft-performance-3.php6) Wind will effect flight times. Get a good 50 mph head wind and it is going to make some difference to having done the same journey with a 50 mph tailwind. Wind at 30,000 ft is fast.
7) Weight also makes a large difference to cruise performance. Higher loads mean requiring more lift. For this you fly slightly more nose up (Makes a massive distance on a long journey) to get a better angle of attack. This in turn means you are on the end of more drag.
8 ) You rarely descend straight in. You usually perform a let down procedure. You can't predict accurately when you will begin your descent because that will depend on the controller and his traffic volumes.
Check the link below, its interesting.
http://en.wikipedia.org/wiki/Flight_plan9) When descending to low level you are bound to a 250 kt speed limit. This depends on the airspace structure.
Economic factors. (The pilot's influence)
1) Should your aircraft be running late (i.e you took off late) the pilot will go faster. He'll burn extra fuel to avoid a costly late penalty.
2) Should you be ahead of schedule (Maybe you got lucky with an unexpectedly strong tailwind) he'll slow down to save fuel.
I would rigorously argue that with all of those factors and more, one would easily have enough room for manoeuvre to prove the earth was round, flat, shaped like a pygmy goat or is inside-out.
Flight times prove nothing.