The fungi (Trichophyton, Epidermophyton and Microsporum) that cause infection on our feet are not black - they are white/cream with brown sporophytes typically.
This will be one of the "black molds". These do not cause infection in us other than sporadically in the lungs if you are very unlucky. They are common in damp environments like bathrooms
Vinegar does nothing to actually kill any molds that I am aware of, but it may slow the growth. Most molds require stronger substances to kill - you could try a quaternary ammonium compound containing cleaner to actually kill them, though even these don't work against many fungi. Bleach/hypochlorite is a sure way to kill fungi, but very harsh on materials. Using a zinc oxide powder and/or zinc undecylate based shoe powder should do the job too. You can often find these at a pharmacy or shoe shop.
The good news is that simply storing the shoes in a dry environment and making sure that they dry between uses is enough to prevent further growth.