Roberk Kirkland is not after RJ.
As I had mentioned in my theory: http://www.whoisredjohn.com/See-a-theory-Red-John/1849
It is very clear that Kirkland is RJ or at RJ's side. I do not want to go over the details, you can read the theory.
I want to explain what Kirkland is doing now.
Remember RJ was always a step ahead of Jane? He did it by getting info from his friends. But this time, friends can't help, because Jane has been silent for a long time. He is not blaming anyone and he doesn't seem like he is planning something. He keeps every idea to himself and tells nobody. So, how can RJ be a step ahead of Jane now?
The only way to do this is to get into his room, take photos of everything he is working on so that RJ can think like Jane and guess what Jane is after. RJ will be able to say "Jane can reach this conclusion with these data, he can't know this with these data..." etc and foresee his plan. This is what Kirkland is doing right now, he is trying to figure out what Jane knows and whether he is very close to RJ. If he is very close, then something must be done before RJ is caught.
The whole process of Kirkland is not study Jane's board and find RJ, it is to be in Jane's shoes to understand how much close Jane is.