What would you recommend for painting this spot on my fireplace where the paint has flaked off from the heat?

Looks like the preparation or primer under the paint may be the problem.

Rustoleum Barbecue Black is made for it

And if ya can’t find Rustoleum, Krylon BBQBlack is great also.
Walmart had the best prices.1200 degree heat range.

thanks everyone. I'll look into those spray paint products.

You can go to your local fireplace shop and buy touch up spray paint that will match exactly.

Easy Peasy

The key to any good paint job is preparation as previously mentioned. Sand the area, feathering the edges and then wipe it down with a clean rag and denatured alcohol to remove any oily stuff. Allow to air dry and if you've picked wisely the color/repaint should be hardly noticeable.

I've used Rustoleum Barbeque Black for many things including exhaust headers. It was better than VHT Header Paint IMO.

Stove paint at your local wood stove shop is a good choice, prep is key.

If you do use stove paint, the first time you light it up, expect some fumes, my wood stove when painted and fired was enough to drive me out of the room.