The first idea I was just black shoe polish, but I’m not sure if that would really accomplish an acceptable fix. The person who wants me to fix them needs them for a formal occasion, so I would like them to look nice.
Any suggestions?
I'm sure. Polish won't fix the pleather, it'll create a nice-looking polished layer over the pleather if you remove the flakes first. I did it with my boots, removed all the flaking and damaged veneer I could and then polished them like normal multiple times.
There's no repairing damaged pleather that I'm aware of, only replacement, but if they want to keep using the shoes, then layers of polish will extend their life, especially cosmetically.