When Kinkel killed his father, according to news reports, it was because he said he would take Kip's guns away. The rule was that Kip would only use them under his father's direct supervision, and according to what Kip told police, his father said he had no choice.
By this time, so much of Kip's identity and self-esteem were tied up in his guns, that the idea was unthinkable. He snapped, and killed his father while he sat at the kitchen table.
From that point on, Kip seems to have behaved like a terrified teenager who knew he'd done a terrible thing and didn't know how to handle it. This seems to differentiate him from many other teenage killers who've afflicted the U.S. in recent years -- though Kinkel was one of the most damaging, there's no sense he got any pleasure from it. It's important to remember that not every teenager who shoots someone is the same.
He dragged his father's body into the bathroom and cleaned up the blood in the kitchen, and then spent an hour or an hour and a half panicking and dithering and trying to figure out what to do. When his mother came home, about six o'clock in the evening, he went to meet her.
According to what Kip told the court, he killed her in the stairway leading up from the garage because he couldn't face the idea of her finding out that he'd killed his father. She never saw the body, and almost certainly never saw her son holding the gun. Later, the police found Bill Kinkel's body still in the bathroom and Faith Kinkel at the bottom of the stairs.
Kip spent the night in the house. Alone, out in the woods, with his dead parents. He played a CD, the soundtrack from Romeo + Juliet, on repeat (it was still playing when the police came the next afternoon).
The PBS documentary show Front Line interviewed several people who knew Kip. A young woman who knew him at school said (from http://www.pbs.org/wgbh/pages/frontline/shows/kinkel/etc/script.html):
The way I think of it, he'd already killed his parents, and I think he didn't know what to do. Like, when he was little, when he got mad, he'd get frustrated. And he gets himself in a corner and doesn't know where to go or- he just doesn't think straight, and he just doesn't know what to do. And I think he really wanted to kill himself, but didn't have the guts to. He didn't- he couldn't do it. He's- I don't know. He's- he's like a little boy. He just couldn't do it.
He did so many bad, bad things -- and even if you think of his killing of his father as a sort of psychotic break, he didn't have to keep making things worse. But I can't help but think of him, in that night, as a scared kid who knew he'd done terrible things that he couldn't undo and couldn't think of a way out of.
Kinkel went to school the next day armed to the teeth. He shot 27 people, two of them fatally. And when the police finally stopped him, he was crying and begging them to kill him.