Kipping pull-ups are one of the more hotly debated traits of crossfit. Kipping is a leg and hip swing that generates motion which makes it easier/ faster to do pull-ups. First I think this is because they are in stark contrast to how most people look at the exercise. Second and more importantly I think too many people spend too much time arguing about stuff on the internet.
One side says that kipping is a natural (from climbing a wall to a kid trying to get up on a tree branch) movement and is thus more authentic. The other side’s primary argument seems to be that it looks funny and then that it is cheating. Having done plenty of both I find the debate stupid and here is why.
Pullups are by far the dumbest exercise to argue over. Close hand, wide grip, palms facing you or away, kipping or not just grab the bar, hang from it and then raise your body until your chin is over the bar. Do lots of them in many different ways.
I think kipping has a couple benefits. First it lets you do more pull-ups faster and get better at them. For most people, because they are fat and or weak pull-ups, which should be a primarily endurance exercise are far more of a max strength exercise as they can just do a few of them. Most people are not willing to do the endless sets of 2 or 3 pullups required to really improve at them. Kipping seems to help people be able to keep going and thus train more and get into better shape. It seems to get people out of a stall of mediocrity when it comes to pull-ups. Also it is a good core exercise.
The kip is just a variation of the exercise, sort of like a push press is to the standard military press. You will need to adjust volume accordingly. A factor of 1 strict pull-up to 2 kipping pull-ups will probably get you into the ballpark. This brings us to one point worth discussing. Kipping pull-ups definitely carry over to strict pull-ups. Also the crossfit people who get made fun of by idiots in videos can almost surely crush those idiots at strict pull-ups. A competitive crossfit athlete who can do 50+ kipping pull-ups can probably do 30 strict ones and a novice who can do 25+ kipping pull-ups can likely bang out a respectable 15-20 strict ones.
Personally I do both types of pull-ups. I also do weighted pull-ups and chin-ups. I tend to keep kipping pull-ups for crossfit style circuit type training where you are doing high volume pull-ups while tired. Do whichever type you like but do a lot of them.