In season 5 episode 16, Bob Kirkland goes out of his way to get information from CBI. The show doesn't show why Gale Bertram gave Kirkland access, so it's possible that he convinced Bertram. 2 episodes later, he asks Jason Lennon whether he remembered him. Just after Lorelei shot him, Jane said that "he knows who Red John is". The only reason I can think of to explain why Kirkland asked that question is because he's scared that Jason can Identify him. Right before Kirkland killed him, he said, "I just hope, that if I'm ever in your shoes, I have a friend close enough to do this for me." Kirkland refers to Jason as a friend and most associates of Red John are his 'friends'.
In season 5 episode 5, a woman named Alexis Shultz(?) asks for updates on the Red John case, normally, it wouldn't mean much, but then she turns to Kirkland and says, "Done." As if Kirkland put her up to it.
In Season 5 episode 7, Kirkland goes to Lisbon specifically to ask her to stop pursuing Tommy Volker. It's later revealed that Brenda was a mole in the CBI. She was the reason Tommy Volker knew about the CBI's moves. She may also be tipping RJ off too and he didn't want his leak to be revealed.
Then, in season 5 episode 19, a Jane's attic is broken into, and a man who looks a lot like Kirkland is seen looking at pictures of Jane's evidence board. His face is never directly seen, but his build is clearly visible.