Hell yeah food can make a massive difference to the skin be it natural commercial or other ??
One of my babies started with skin irritation/constant scratching at 6 months old and I have been on a 3 year plus journey to perfect his condition, I have now mastered it with a massive amount of commitment, cost, trial and error. His drugs however are very costly and I don't know if most could or would fund them ?
Anyway way back at the begining both the vet, holistic vet and dermatologist (consulted these all at different stages) all put Harry on an elimination diet which consisted of a noval source of protien and carbs only, Nothing else at all, no treats, no veg, fruit, nothing but these two foods he had never been exposed to before for a 12 week period, during this period if you see an improvement in the skin you have a indication that the cause or some of it could be food allergy.
In our case ours was/is not food allergy its atopic dermatitis which is much harder to treat (but there is hope with this costly wonder drug Harry is on) but the next process after this if there are some indications that certain foods are the cause is to gradually introduce one at a time new foods, so maybe give carrot for a week and see what happens then beef the next week and so on and it takes beepin ages and a lot of coomitment but well worth it if you can eliminate the source of your doggies bad skin thus making them a happier healthier mate.
Now if its found that in this time there is no change to the skin condition you can assume there is another cause and investigate this appropriately with your vet or dermatologist. Usually the next best step is intradermal testing.
Now without sounding like a bitch and a nag if your dog has had bad skin as you say for ages get it sorted properly. Obviously it depends on your defintion of bad and how much it bothers him and I do not wish to sound like I am having a go at you or assuming that you are not attempting to get it sorted but... it hurts so much to have bad skin and he can't tell you that and it can literally drive you insane to not feel comfy in your own skin because your itchy and or sore etc etc.
Please take this info with the love its intended and if I'm barking up the wrong tree disregard my dribble but I am trying to help.
Good luck with it all.