It's all good! It's normally the cereals and fillers in commercial food that can give bad coats and itchy skin, so cutting all that out alone is normally enough action to see a huge improvement in coat condition.
If you have a VERY sensitive dog however, beef may need to be avoided as this can sometimes be problematic for dogs with skin issues.
Plenty of oily fish - salmon, mackerel, sardines, sprats etc - is especially beneficial.
agree with all of the above but you can also supplement their diet with salmon oil from fish4dogs.
i swear by the stuff. i even gave 100ml of my 500ml to a friend who has 2 commercially fed whippets and within a few days their coats had totally changed and both were silky smooth and shiny just like my boy.