In our association Kiai is not taught, but many people do it.
It seems that it slowly occurs naturally for some people, and in others they develop other ways of achieving the same thing.
I found that Kiai came quite naturally to me, as my breathing is a very important part of my technique. I initially found that making noise whilst breathing reminded me that I had to lol
it sounds funny but I am amazed at how many people actually forget to breath, especially during randori. I see their faces turning blue because they have tensed up and forgotten to breath. But making noise during training means that I associate the breathing with the movement and so I naturally dont forget.
Which over time developed into kiai on the execution of some more dynamic movements.
I heard my sensei once remark that people only really understood kiai or did it naturally after around 5 years of practice. he didnt expect to hear it from anyone who had trained less than that.
thats my 0.02