Shoe polish will work great, just use a semi abrasive medium to scrape off the flakes first so everything is smooth, a bristled shoeshine brush is made for that, and then apply shoe polish, buff, shoe polish, buff, repeat, eventually, you will literally see your reflection in them. if you want to go that far.
It takes time, but they will look great, that's what shoe polish does. You can also bring them to a professional shoe repair shop and they'll shine it for you if you don't want to spend the time and have an extra 50ish bucks.

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