I haven't listened to Jon's song you refer to, but from memory I think the opening riff in LW's Blues with a Feeling is just a trill. Not a clean trill, and not moving completely from all of one note to the other. Just a small sloppy trill always picking up both notes. Thats what I hear anyway.
One thing you hear all the time in Chaicago blues is a tongue trill where the player is moving his tongue back and forth quickly from one note to another, for example from 1d to 4d. This is hard for some people to do - I can't do it yet.
OK... I listened to Jon's version of People Get Ready. In the midst of the song, he did his "Train Whistle" (as he called it).
There was a sound he produced there... like a vibratto, but I think it is something else. I hear this sound a lot with Chicago Blues toungue blockers. I was listening to "Blues With a Feeling" by Little Walter last night. The opening riff used the same technique (I think).