you don't really want the plant growing on the flue as if it gets behind it and gets thicker it will damage it . if you were to get a half circle fine wire cage screwed around it the plant will grow and hide it without hurting it . keep an eye on the outlet and make sure its always clear .

Double walled flue pipes, if thats what you have, don't go up to kindling temperatures but my advise is to leave it alone and leave it as it was installed. Ok, the looks of it is not that great but you don't want to do anything that would give the impression of fire and building code tampering should a combustion problem develop. Don't give the insurance claims adjusters an excuse not to approve a claim.

to be quite honest I agree with ls .

Quite honestly you shouldn't be encouraging anything to grow near the flue. Adhesive climbing plants will find the slightest weakness in the joints of the pipe and you will have a blocked flue before you know it - except you won't know it because it will be hidden under vegetation. Vegetation will also mean that air can't circulate and the flue won't dry off properly and even stainless steel can corrode.
The flue installer should have told you this!