I haven't heard of this exact type of thing happening to someone after a stroke. Two things come to mind, however. The first is that he could be having pressure sores or stasis swelling from not moving the arm and leg (I am assuming that the dryness is only on the side affected by the stroke). The second is that he could be having some decreased perspiration from lack of neural input to the sweat glands on that side. Again, I haven't seen anything to the degree that you are describing, so this is merely a guess.

If the first item is the cause, then he would benefit from range of motion exercises and soft support under the areas of his arm and leg that lie on a surface (such as from a very soft blanket or pillow). For the second, there is not much else to do but, as your dermatologist recommends, put moisturizing lotion on the extremities.

There is a saying in dermatology: "Thousands of diagnoses, only two creams". To a first order approximation this means that if something looks dry, it needs moisturizing lotion. If something looks too moist (with fungal infection resulting) it needs a drying powder like "baby powder". It sounds like he could use some moisturizing lotion.

I would follow the direction of your Dermatologist, as in many ways this is more of a Dermatology diagnosis than a Neurology diagnosis. If you don't like what your hearing, try seeing a different Dermatologist.

As for the breakdown of chemical components, I have not heard of that happenening after a stroke.

Good luck!