I believe I've waited enough time for responses. 
Victory for RE.
Absolutely. When I first heard about this I did the same thing and checked flight times from the horses' mouths for flights corresponding near enough equal distant from the equator. I did Johannesburg to Perth for the Southern hemisphere and Cairo to Shanghai for the northern hemisphere. Now the Cairo flight is approx 500 km further above the equator than Johannesburg is below the equator, but Shanghai is further away from Cairo than Perth is from Johannesburg so it roughly evens out. Airlines were Egyptair and a South African one (forgot the name).
Here they are:
West to East
Cairo to ShanghaiDistance: 8125 km
Time difference: -6 hours
Depart: 23.40
Arrive: 15.20
Time for flight: 9.40
Johannesburg to PerthDistance: 8303 km
Time difference: -6 hours
Depart:22.35
Arrive: 13.25
Time for flight: 9.50 hours
East to west
Shanghai to CairoTime difference: +6
Depart: 00.30
Arrive: 5.30
Time for flight: 11 hours
Perth to JohannesburgTime difference: +6
Depart: 23.50
Arrive:5.20
Time for flight: 11.30 hours
The debate is over. There is no flat earth, at least for all practical purposes.
Now, let's dissolve these threads and change it into a new theory instead shall we? Or are we going to be extremely stubborn mules? I suspect the latter.
I was about to do the same for South and North America, but after the above there is no need to. The only way FE would now work is if you start completely rearranging the UN map which makes the FE unworkable.
Good luck boys. I know you'll need it.
