I would be bewildered if the FBI doesn't have a back door into every messaging app allowed on american cell phones. That being said there is one chat app that cannot be easily broken by the FBI: Pictochat on the nintendo DS. You would need an FBI agent with a nintendo DS searching for chat rooms in physical proximity to the communicators.
I'm not sure if this is 100% serious but if it is, how could the FBI having a backdoor into every messaging app fit in with the relative ineffectiveness of the FBI?[0] If they truly did have the ability to spy on any messaging app without issue then you would expect them to have far more success than they actually do. For comparison, a quick Google search says China has a 99.9% conviction rate. Remember security and intelligence agencies also want people to think they are some omnipotent and omniscient entity that you cannot escape from, even though we know this is far from true[1][2].
This is kind of a nitpick, but U.S. prosecutors also boast 99+% conviction rates. Note that conviction rate is not necessarily indicative of a systems effectiveness (or lack of fairness). Prosecutors only pursue charges in very few cases, and very few of those cases go to trial
The first link I mentioned says in 2017 the conviction rate of crimes referred to the Justice Dept. by the FBI was 47%. Of course I am guessing the differences here are definitional, regardless the stat was just used as a broad proxy for how successful the FBI is in getting people they think are criminals convicted.
