Most adhesion failure (peeling) can be traced to inadequate surface prep. A shiny or chrome surface doesn't give the paint enough mechanical adhesion, and the paint will delaminate.
Best prep is media blasting. Not aggressive enough to rip off any adhered chrome, but aggressive enough to frost the metal or plating. Then it needs to be cleaned. Many metal prep products will not withstand high heat, so washing liberally with denatured alcohol is probably a good choice. Don't wipe a blasted surface with a rag, or it will deposit lint.
I've used VHT High Heat Paint, and didn't care for it. Very flat and chalky. Turned brown-ish eventually.
My favorite is Rustoleum High Heat Ultra -
https://www.rustoleum.com/product-ca...gh-heat-ultra/
It's a semi-gloss black, covers well, and seems to hold-up better than others I've tried. They also make it in silver.
Professional ceramic coating is the best, but needs to be done professionally and is rather costly.