Can the pipe be in contact with furnace flue?
Give this a look I did have time to read it Sorry.
No. It looks like type-B vent which needs 1" minimum to combustibles and I’m sure that rubber coating burns.
here is more info http://www.gastite.com/homepage.php?pg=builders
The main concern is arcing between the pipe and exhaust flue during lightning events.
yes, arcs do occur from bonded metal to bonded metal if the charge is high enough since the actual bonding point/resistance comes into play.
The chance of that jacket or strap igniting is very minimal but that is also a valid issue.
See any melting yet?