If I were to speculate (my opinion only, etc)...
Theory: Burke got JB some pinapple from the kitchen, and perhaps got out the flashlight at this time to look in the basement for presents. The two got into an argument over something and Burke decided to whack her with the flashlight (this seems all too possible to me, as my brother once whacked me in the head with a baseball bat). Dad and mom, for various reasons, and seeing how injured JB was, decided to cover it up. I suspect that Dad came up with the fake abduction and ordered Patsy to write the note while he took care of JB.
Why the cover up?
Dad: I suspect that dad had been sexually abusing JB for some time. He would have known that JBs abuse would be discovered in an autopsy, and I believe he hoped that the violent vaginal trama inflicted on the body would conceal this ongoing abuse from investigators. Dad clearly was the one who dressed JB, as mom never would have put her in these ridiculously oversized panties. Mom, after writing the note, probably brought her some of her favorite things.
Mom: would have been easy enough to convince. She obviously would not have wanted to lose both children, and quite possibly believed that Burkes behavior was linked to her own illness. Mom seems the obvious author of the note, not only because the writing and wording match well enough, but because John never would have written anything that ludicrous.
Burke: under this scenario Burke's behavior was more childhood idiocy than sociopathic and evil.