The suspect who killed UnitedHealthcare CEO Brian Thompson handled his gun proficiently during Wednesday's shooting -- something that's painfully clear, according to a former FBI agent.

Jennifer Coffindaffer spoke with us on "TMZ Live" Friday and broke down the suspect's expertise -- pointing out how he used a silencer on the gun, fully aware it could cause jams, and cleared it like a pro without missing a beat when it did.

Watch the video ... Coffindaffer digs into the suspect’s firearm skills and breaks down what the 3 distinct shots reveal about the man behind the trigger.

She also unpacks his days-long stay at a NYC hostel before the murder, pointing out how odd it was that he didn’t spring for the privacy of a hotel room. Then there’s the pre-murder Starbucks stop -- another bizarre move she says hints at his detached state of mind.

Jennifer suspects the assassin has likely skipped town, but when it comes to whether the cops will catch him, she’s crystal clear on her take.