Two things...
Maybe your dogs food isn't cutting it in the coat department.
Not saying it's the greatest by any stretch, but my chocolate (Rowdy) had the prettiest coat I've ever seen on a chocolate and all he ever had was pro plan performance supplemented with rabbits in the back yard.
No joke though...everyone commented about his coat.
Our JRT, (Penny) has had allergies her whole life. The itchy scratching variety.
Never any dandruff to speak of, but last week after mowing, (she loves to follow me around the yard), she had a major allergic reaction.
She just could NOT quit itching.
Anyway, after a little google time, I started supplementing her with fish oil and it has made a world of difference in this dog.
I know it's early, and it's not supposed to work that fast, but it is undeniable how much less she itches now.
Do your homework (or better yet, consult your vet) before you just start giving your dog fish oil though.
Best of luck!