A1 crosses midcourt. B1 slaps the ball away. A2 kicks the ball to keep it in bounds and has a breakaway layup? Is this a kicked ball?

Rule 4-29 Kicking the ball is intentionally striking it with the knee or any part of the leg or foot below the knee.
Violation whether done by offense or defense.

Good Question! I had a slightly different situation last night in a JV game where the offensive player was driving to the basket, lost the ball and the ball was bouncing around on the floor at the feet of all the players. The ball bounced off some feet unintentionally a few times. After bouncing around, a defensive player seemed to kick the ball like a soccer ball and I called a kicking violation. The defensive team's coach disagreed but I told him I saw what I saw and I am certain I made the right call. However, it would be good to go back and look at it because like the original poster, I forgot the specific definition of a kick!! ;)

An intentional kick in both those plays would be a good call.