I won’t repeat what’s been said above because they’re all very good answers, but I’d just like to add: once or twice a week I mix a drop or two of olive oil in Lily’s food, which I think helped with her dry skin. Just make sure you don’t put too much oil, as it might be problematic too. Some other people swear by flaxseed oil, but I’ve personally never tried it.
Also, I don’t know if it’s just me being a paranoid mum, but I give her footbaths once or twice a week also. My brain thinks clean feet = less chances of skin infections that are brought by scratching.