To be clear, kicking with ankle weights is damaging. So is running with ankle weights.
If you want to do slow kicks with light ankle weights that might be ok, but it's not really going to make you kick harder. Let me explain.
Doing a slow movement with light weight is going to build endurance for doing a slow movement with light weight. This won't translate to explosive power, and it won't increase your total strength any. There is no real purpose to do a slow movement with light weight if your goal is strength development. I would be willing to bet that two people, one who only does normal kicks against pads or whatever, and the other guy who does the kicks against pads and who does slow movements with ankle weights, they are both going to kick exactly the same force. The closest analogy I can give is that, if your goal is to be a sprinter, running long distances does nothing to help, because the energy systems involved are so different. If you want to kick harder, make your muscles able to generate more power. Do this by lifting heavy weights (deadlift, squat). If you want to kick faster, just practice kicking.
Doing bodyweight squats is ok if you don't want to lift weights or don't have access to them. They will develop strength until you get past a certain rep range, in which case they will just develop endurance in the legs (which may improve your fighting). Think of it like this. Consider a total beginner who can only do 10 bodyweight squats and who can only squat 50 pounds. If this guy does bodyweight squats, when he gets from 10 to 20 bodyweight squats he will probably be able to squat slightly more weight. When he gets to 30 bodyweight squats he will probably be able to squat a little more weight. When he gets to 2 or 3 sets of 20 or 30 bodyweight squats, he will probably be able to squat a little more weight. If he gets to 50 or 100 or 200 or 300 bodyweight squats, it won't make him squat extraneous weight. Thus, your training should be based around your objectives.
Something is better than nothing, but if your goal is to kick as hard as possible, you need:
1) proper body mechanics
2) the ability to generate power
The first can be achieved by training
The second can be achieved by weight lifting
This is my overly verbose explanation of what is basically a basic question