Here is the tools for the job.
A wire bristle brush
and a can of 'derusto' Hi temp rust paint..
any paint exceeding 1500f* degrees will do...for extreme temps.
I prefer the rusty paint,
you don't want to use regular black spray paint, it will not transfer heat properly, carrying heat farther down the exhaust.. nor will it stick as well.
I got lucky and found hi-temp rust paint for like rusty automotive headers..
but i haven't found a pic online yet.
I always use the wire brush and rusty part
under a water bath, like a outdoor faucet, to keep down the rust inhaled...yuk
and
paint dust is HARMFUL.
Wear a respirator.!