There are kites that flap in the wind, which looks nice but is just for show: the wing movement doesn't do anything for the kite except waste a bit of air. This idea is for a kite that stores energy input from the operator on-the-fly, then releases it to gain (or retain, when the wind is low) altitude.
coil spring is wound up by repeatedly pulling the kite string, varying between a medium (normal) tension and the (first few inches of the) heavy pull used to gain altitude. (Not completely trivially, the wings will passively flap as they wind up the motor.
Subsequently, when the line is slacked (through operator control or dead air) it will flap until it runs out of juice or the line tension is back to medium.
Bank some energy when the wind is good, then release it when desired.
You can also use the mechanism to launch: wound up on the ground then released, the kite will climb to altitude flapping wildly, even on a calm day, like a hunting falcon from a glove.