The speed increase from kicking with ankle weights and then removing them doesn't demonstrate any improvement. It demonstrates that it's easier to kick correctly and quickly without adding resistance. The fact that the kicks feel faster than before using the weights doesn't prove anything.
Don't kick with ankle weights. If you want stronger legs, then use an actual strength program that involves squatting, deadlifting, and lunging with a barbell. If you want stronger, faster kicks, then...use an actual strength program that involves squatting, deadlifting, lunging, and Olympic lifting (e.g. power cleaning) with a barbell, and kick a heavy bag a lot. Ankle weights are not the answer.
First, ankle weights don't provide resistance in the correct direction. The ankle weight is acting against gravity, not just the line of force of a kick. If that's what you want, why not hit a heavy bag?
Second, they raise the risk of injury by making the fast movement harder to control and more likely to stress the joints.
Third, because the activity of kicking with resistance is very similar to kicking normally, it can interfere with developing speed, speed-strength, and technique efficiency in general. Fourth, why are you kicking with ankle weights when there are other, better ways to get stronger and more powerful in that movement?
If you want to kick harder then you need to develop basic general strength first. This means you should start a basic strength program, probably with a barbell and weights, using fundamental exercises like deep squats, deadlifts, and lunges with a barbell. Once you reach some basic strength benchmarks (deadlifting 1.5x bodyweight, easily squatting many times with a barbell weighing as much as you do), incorporate power versions of the Olympic lifts like the power clean.
I find that things like ankle weights are like "lose your belly in 30 days" weight-loss products: they're seen as an easy alternative to learning how to lift weights properly. A general strength program will be enormously more productive for you than kicking with ankle weights.