There was a doctor in Seattle who once told me that he could "cure" my skin by a rigid diet and extensive vitamin therapy. Essentially, it was what any "diet guru" might tell you, i.e. no refined sugar or flour, etc. The number of pills I would have to take a day was a lot, something like a dozen. Suffice it to say, as a teenager, I was unwilling to give up pizza and junk food and never tried it.
I do know that when I find something that works, like flax or a new soap or lotion, it only works for a while and then it just kind of fades away. The stuff that DOES work is plain old fashioned work. Long soaks in a tub with just a little bath oil and then a good pumicing or the old standard of a good long sweat.
I will say this, if you have a diagnosis of Ichthyosis, the roots of the disease are in your DNA, not your gut. Diet or supplements might improve the appearance, but they won't make it disappear. If you can live without dairy, give it a try and see if it improves but don't expect a miracle.