He does it loads of times. They kiss atleast three times. Karino kisses him in the end of chapter 2 and Karino kisses him in chapter 3. Also in the creepy teacher chapter, Karino kisses Azusa. I don't think that Azusa had initiated a kiss with Karino yet.
Ah, you're right
You know at the end of that "creepy teacher chapter" the teacher said wanted to join the game so he could do things to Azusa? I don't care how dirty this sounds -- I kinda wanna see it happen XD But don't worry, I'm not gonna ruin anyone's ships.
Ya know, I just realize that since I read this, Karino almost never kiss Azusa. Scratch that, I haven't see he kiss Azusa, yet.