Is the FBI investigating him for making threats?
Sure they are.
See or hear something ( that's us)
Do essentially nothing about it after studying it (that's them)
P.S. I heard a former US Marshall on FOX NEWS say that the FBI should be disbanded and replaced with a expanded United States Marshall's Service with the Investigated Data Based parts, Research and forensic sciences parts integrated into the Marshall's Services. Sounds right to me after they way they have botched everything they have touched recently including our rights.