If you're looking for a Black owned Minecraft server, then I'm not too sure if there are any to be honest; I don't think Minecraft is that popular with Black children as much as it is to White children, or adults. Black children/adults usually like to play less creative games from my experience; like 2K, Call of duty, Need for speed, etc... Not that that's a bad thing, but It's just what our demographic is more interested in.
Also, it depends on if you're on console or not. If you're playing on a console, then you probably cannot join any specific Minecraft servers that you find on the internet, because on console they do not allow you to do this (probably for safety reasons). On PC however, they do allow you to join any random servers you want to that you've found around the internet by putting in an address for it, so you possibly could find at least a few Black owned and run Minecraft servers out there, but I'm sure that that's going to be extremely rare to find, and if you do eventually find one that's Black owned, then it's most likely not going to be that popular; with probably at the minimum a few players on the server sadly.