I need help. I wonder how the mod stores the custom skins the player wanted.

From what I've seen, regardless of singleplayer or multiplayer, it's stored in the each player's .dat as "fabrictailor:skin_data" (so yes, you can have different skins for each world and server).

You can check it in "'minecraft-folder'/saves/'world-name'/playerdata/'uuid'.dat" (client) or "'server-root'/world/playerdata/'uuid>'.dat" (server) with a text editor, or some compatible program like NBTExplorer, but it mostly look like this:

Or if you have it installed client-side, you could take a look at this #60

Edit: the ones in quotes ' ' is interchangable

No worries, I used to wonder the same thing as you. It wasn't until I need to recover a friend's playerdata that I accidentally stumble upon it :)

That's exactly my case! I wonder if I could build a Minecraft scene in Blender, but when I asked my friend for his skin, he lost it!

Thank you very much! So sorry that I didn't view the source code before I open the issue.