See
here for some opinions on Dr Johns food

The dry skin issues would almost certainly point to the food are you are feeding,dr johns is extremely low in protein and fat,it lacks meat and is very high in grains/cereals,all of the things i avoid like the plague in dog foods,all in all it is a very poor food :(
Get rid of the baked beans,and substitute the tuna with tinned sardines,pilchardes,mackarel etc,all are healthier and have higher Omega 3's than tuna,which has ben linked to high mercury levels,tuna is the one fish i would not feed.
I would change to a super premium food,avoid foods such as bakers and most brands by Purina,hi life,gusto etc,and pretty much any supermarket food,although there may be one or two exceptions such as autarky which i believe is available in some supermarkets.Look for a food with NO colours,dodgy preservatives(bht,bha,ethoxiquin),it should have meat as the first ingredient and as least grains/cereals as possible,these are just used as cheap fillers and provide to nutrients to the dog,a little bit of rice however wont hurt.
It is also a good idea IMO to add a variety of fresh foods to their diet,such as meats,raw meaty bones,left over veg,fruits/berries,tinned fish a bit of organ meat here and there,cottage cheese,yogurt,Raw eggs are also excellent for the coat and are a great source of protein,the list is endless.My dogs rarely get just plain dry food,i always mix in healthy extra's.
Once you have changed foods i would give a good quality fish oil along with vitE,which should help with your dogs coat.But remember all the supplements and healthy extra's in the world are not going to help if the base food is of poor quality.
Good luck :)