Which action is least likely to cause flat wheels for a train operator?

Braking gently before a curve is the least likely action to cause flat wheels. When a train operator applies brakes gently, it allows for a smooth deceleration, which helps to evenly distribute the forces on the wheels and minimizes the risk of skidding or locking up the wheels. This gentle application of brakes is particularly important before entering a curve, as it helps maintain the train's stability and track alignment while ensuring that the wheels remain in contact with the tracks without excessive friction.

In contrast, exceeding allowable speed on either straight track or curves can lead to significant forces acting upon the wheels and may cause them to slide, resulting in flat spots. Abruptly stopping at a station can similarly create a sudden jolt that increases the likelihood of wheel skidding and damage. Therefore, the action of braking gently is more favorable in preventing wheel flats compared to the other listed actions.