There is nothing to book - you just go there.
But Kiyomizudera is not the best place to see cherry blossoms in the area. There are far better places in Kyoto. The thing is, all are pretty popular, so you might see more people than petals.
If you really want to see cherry blossoms, you really need to go to lesser known gems. One excellent place is Sewaritei in nearby Yawata City. Or, go to the mecca of cherry blossoms at Yoshino in Nara. Lots of people, but it is a whole mountain so there is still lots of room. There has been poetry praising the place for over a thousand years.
You can’t book anything. It’s open space.