I don't feed any exhibition chickens, but my exhibition ducks get a 20% poultry food, oyster shell, greens, flax seed, and a very very tiny little sprinkle of dry cat food.
20% protein is plenty of protein. The flax seed is oil producing and I give it for oil on the feathers. My ducks feel armor plated, their feathers are so hard and well oiled. The cat food is NOT for extra protein; it is used as a source of animal protein.
Perhaps show chickens need extra protein while they are growing a new crop of feathers, but even for growing feathers 20% should be plenty of protein. If your birds can not grow feathers with 20% protein, perhaps you should add some genetics for better feathering.
I'm feeding an expensive dry cat food right now because it was on sale for a very good price. Normally, I buy the cheap brand that is made of fish meal and a lot of grain. I want the ducks to have fish and the grain is fine for them (not great for cats, though). If you don't want the chickens eating fish, then you can buy cheap dry cat food made from meat meal.
I suggest that you only feed cat food, or dog food, as a small part of the diet. More like a daily treat than a meal.
I don't know why you want an enormous amount of protein, but you can buy turkey/ game bird feed that is 28% protein. I use it for the first week with ducklings and I use it to start Cornish Cross chicks. It's made for poultry, so should be balanced nutrition.
For good feathering on show chickens, I suspect it is more important to limit the time they spend in the sun and to keep dirt off of their feathers. Also house them so that other birds don't peck their feathers.
