If you would like to get better at kipping or butterfly pullups, there are two key components that you have to work on: strength and technique. This shouldnt be shocking to anybody, although most people forget that in order to be more efficient at these two styles of pull-ups, you need to be strong enough to control the movement.
The general rule of thumb is that an athlete should be able to do 3 strict pull-ups before learning the kipping motion. This is to ensure that there is enough musculature around the shoulder joint to keep everything stable and in line, preventing wear and tear on the ligaments and tendons. If you do not have 3 good, strict pull-ups in a row, this needs to be your first priority.
Practice a few sets of 10 with a band after class, 3 times per week. You can also build a good amount of strength with negatives, but you have to be careful not to overdo it. You can do just a few (2-3) sets of 5 slow negatives, 2 or 3 times per week. Use a box to jump above the pullup bar, and then lower your self back down to the box slowly.
If you can already do 3 strict pull-ups, you should still look to continue building strength. Practice sets of strict pullups often, and once you can complete 3 sets of 15, use a weight vest, medicine ball or a belt with kettlebells attached to make them into strict weighted pull-ups.
In the meantime, you can practice the technique for kipping often. If you aren´t doing 3 strict pull-ups yet, practice the gymnastics kip from the pull-up rig just once or twice a week, making sure that you are in an active shoulder position always. You can also practice drills from the floor, one drill being the barrel jump into a back bridge. Ask a coach if you need a reminder as to what this looks like!
If you have the strength, practice kipping pull-ups outside of class to make sure you have the coordination and timing down under low intensity. Your goal should be to complete 15-20 repetitions in a row without losing control at any time. Once you can consistently hit 15-20 reps at a time, you can begin to learn the butterfly pull-up.