The first association with "Flying tank" would be Soviet WWII close support aircraft: Il-2 Sturmovik. It was hard to kill and it was efficient tank buster. However, in this case I mean literally: flying tank.

In late 30's idea of an airborne insertion of combat vehicles behind enemy lines appealed to the military commanders of several countries. Light tanks "falling" from the skies would be unexpected and nasty surprise for enemy and perhaps that little extra push which make a difference between a victory and defeat. Russians were experimenting with large bombers: combat vehicles were embedded into bomb bay of the aircraft, so it has enough clearance to take off. German approach was different: they were building large gliders, capable of hauling small combat vehicles and even light tanks.

An original idea came from A. N. Tupolev Bureau: a T-60 light tank was fitted with wings and control surfaces, so that body of the tank was a backbone of the resulting glider.Amazingly, this project advanced beyond paper and was flown in 1940.

The glider had an unorthodox control system: an inclination of the gun was slaved to the tail surface (pitch control) and rotation of the turret was used to change the roll. Prior to landing, a pilot/tankist would start the engine and speed up the caterpillar, so that KT-40 can land.

No KT-40 went into production.