How to do Kipping pull ups:
Step 1: work on strict pull-ups until you can do 8–10 unbroken. Without the shoulder strength needed to do unbroken sets of strict pull-ups, the aggressive / dynamic motion of kipping pull-ups risks injuring your shoulders. Not worth it! I’ve seen many athletes skip this step and hurt themselves, as well as many others who did focus first on strict pull-ups and moved on to kipping pull-ups safely and effectively. (I’ll skip techniques for achieving step 1 as it’s an answer unto itself, and assume that you’ve already gotten to the point of getting strict pull-ups. If you haven’t, and would like tips, ask a separate question about this.)
Step 2: hang from the bar and practice a kipping swing without the pull-up action. Control your body weight from your shoulders/chest, keep your feet together at all times, and swing your legs back and forth so your body alternates between a concave and convex curve shape. On the back swing, your knees are bent behind you and your chest is out in front of the bar (you can’t see the bar). On the fore swing, your legs are in front of you and you push your chest backwards, so you can see the bar in front of you. Aim to stay in control without getting “loose” at your shoulders, but try for a smooth, fluid motion. Do, say, 3 sets of 10 swings to warm up and start building muscle-memory.
Step 3) add the pull-up. It helps to watch another person do kipping pull-ups well or to watch a video so you know when to pull and how to “recycle” your energy into the next kip. There are two main variations on kipping pull-ups: one is more advanced than the other.