I think there might have been two crime scenes, bedroom and basement.
I do think that Burke may have caused her head injury, but not in the kitchen. He's down there having snack, and here comes his sister, wanting some. Maybe he gives her a little, maybe she steals it. Whatever. He's irritated, or maybe he's fine with sharing. So he walks her back up to her bedroom. He's using the flashlight to navigate so as not to wake up his parents and get yelled at. He plays a little doctor with her, and this is where things go wrong.
Maybe she wants to follow him to his own bedroom and cuddle. He doesn't want this because she's a bedwetter. Or he wants to play with his new toys in privacy, without an annoying little sister getting in the way. Maybe she's just being loud and silly and he's worried that their parents will wake up and be angry. Maybe they get into a sibling spat over nothing. So he smacks her with the flashlight.
I keep coming back to Patsy in JBR's room, asking the detectives if they saw blood on the bed. Why would she worry about blood? Because that's where the original injury happened.
At this point, Burke either waits a bit, hoping that she will wake up and he is not in trouble, or he immediately runs for his parents. He confesses everything, including the doctor playing, and the cover up begins.
JBR is moved to the basement while they try to figure out what to do with her. Either Burke is forgotten in the panic, or he is told to stay out of the way and disobeys. At some point he pokes at her with the train track. Not out of meanness, but in a desperate attempt to revive her. Please, Sister, please wake up. I didn't mean to hurt you so badly.
At some point before the strangulation, he is sent back to bed, where he remains. When he is woken up in the morning by his parents peeking in, he is hopeful. Is his sister alright? Maybe it was all a bad dream, or JBR has woken up and is ok. He runs downstairs and asks what happened, but his mother is on the phone and quickly hushes him and sends him back to bed.
Before the police arrive, one or both parents come upstairs and impress on Burke how important it is to claim he was in bed the entire time. If anyone finds out the truth, they will take him away. He will be sent to a place for bad kids and they will hurt him there. He will never see his parents or be able to come home again.
I can see a 10 year old boy striking his sister in an act of rage. I hit my own sister at that age, though not with an object. I can not see a very sheltered 10 year old being able to perform any sort of cover up, nor do I see him strangling his sister.
Where I'm all getting to with this is that one parent is in the bedroom, looking for blood or any other signs of what has happened. That parent grabs the flashlight and takes it back to the kitchen, where they write the ransom note. The other parent is downstairs, assaulting and ultimately killing JBR.
They each have their own plan, and are on two different floors staging, which is why it looks so disjointed. By the time the realize this, it is either too late, or they can not agree on which plan to follow. So they call 911 and hope for the best.