At first, I didn't think Chrissy would ever be a rat, but after multiple viewings on the final season, I actually think he did flip. But, I don't think the FBI caught him for the JT murder. Chris didn't want to get caught for that - how would you explain the fact he made sure he didn't leave his fingerprints on the doorknob.
However, if one recalls, at the end of the episode Christopher comes home to a yard that is completely wrecked (by Paulie), which is symbolic of the state of Christopher's mind and soul at the moment. Right before he enters his house, Chris stops and rights a tree (one could say he "flipped" it - right-side up) that had fallen on its side. I believe this stands for Christopher's final decision to flip on his own will. He went to the FBI - they didn't come to him.
But, he didn't have much time to inform the FBI of Tony's greatest crimes, as he is killed one episode later. Tony's luck subsequently changes at this very moment - notice how lucky he is in Vegas later in Kennedy and Heidi. The change of fortune is that Tony made the correct "business" decision in killing Chrissy, no matter how dreadful that decision was to his blood family.
Christopher may have very well been the one "giving grand jury testimony" Tony's lawyer mentions in the final episode.
