I agree with shihonage. Aikido is the kind of MA which requires the least energy involvement from Nage. I find it difficult to Kiai, even if I wanted to. Sometimes I Kiai when I am being violently thrown by a powerful Nage, but maybe that's fear :-)
When I was doing Judo, I used to Kiai all the time. In Aikido, when you really commit yourself to throwing, Kiai comes out naturally with techniques such as Kokyu Nage, Koshi Nage, Kaiten Nage....etc. Rarely with Kote Gaeshi when I should be mindful about my Uke's wrist rather than the power of my throw, or with pins for example. It would be funny to shout a loud Kiai, while throwing Uke softly.
This said, I would like to add that I usually try not to Kiai so much, even though Sensei encourages this, but people in my dojo are shy and rarely do it, so I feel kind of odd. Moreover, if I Kiai too much, I get a sore throat ;-)