I'm going to ask the Mods to move your post to its own thread in the Cat Care and Grooming forum: http://www.thecatsite.com/f/6/cat-care-grooming. More people experienced in this problem will be likely to see it that way and you should get more suggestions than here. Please keep posting in this thread, though. It's for whatever is on your mind and our cat's wellbeing is right up there!
Good luck! I hope you find a solution for your kitty.
I'm giving my cats little olive oil now and then, they like it as a treat, very tiny amount should help already. We have so dry air here because cold outdoors and heating indoors most of the year that it makes human skin dry too, I haven't had so much issues with dry skin after I started using olive oil in cooking.
Another thing you can use olive oil is baking, after kneading when you put dough to rise, put tiny amount of olive oil to hand and rub it to dough so that dough has nice shiny surface, it keeps dough from drying and you get prettier breads, also helps with flour causing dry skin issues.
You can still sprinkle (I rub flour a bit to bread after sprinkle as I don't have proper tools for sprinkling) flour on top of breads after putting them to oven tray to get that nice extra flavor.
Some don't like olive oil taste, but there are some olive oil bottles that don't have much of any extra taste, I use Bertolli Classico and it does not add taste to meat unless I put really really lot of it.
Dry winter air causes dry skin in people and animals. Using a humidifier in your home will help. Use a cool mist one, not a warm mist one to avoid potential burns to you and your cat.