A "control flight" is in reference the they claim that pilots know how fast they are flying because sometimes they are not flying on the fastest route. They are always using winds to reach their destination, which is why there are two paths to the same destination in the previous image I provided despite significant differences from the optimal dotted line RE geographical route.
It’s important to understand that wind speed is not some unknown quantity to pilots. Wind speed can be derived from a number of sources, and many of them make no assumptions at all about the shape of the earth. Inertial navigation, technology that predates GPS, can give very good measurements of groundspeed, from which wind speed and direction can be calculated either manually or automatically from the aircraft’s airspeed data. Overland routes, or routes flying reasonably close to coastlines or islands can also derive groundspeed from DME or TACAN beacons, typically out to a range of 100nm or so. Neither of these require any presumption of a coordinate system, or earth shape, to function effectively.
The important point to hoist aboard is that, when compared with, say, GPS derived data, pilots aren’t presented with enormous differences, which would have to be the case if the known distances between points on the earth’s surface were radically different to the conventional RE model, as they must be if FET in any of its guises is true.
So trying to explain away the differences with vague terms like ‘anomalous winds’ is a deeply flawed argument, because pilots know what the wind is doing - and it never gets large enough to make the speed-distance-time calculations work for FET distances. Furthermore, all of the flight data is cross checked - distance to go, airspeed, groundspeed…and it always matches known distances.