Farm Sanctuary, from whom we've gotten much advice, originally had a recipe of corn, oats and sunflower seeds with a dash of grit that they fed their chickens. They found this didn't work well because the chickens just picked out what they want. So the California branch switched to a crumble (Manna pro commercial layer 16), which is basically little pellets made from mashed-up ingredients.
You want a pellet that's 16 to 20 percent protein. Feathers are made from protein. So if your birds have been abused or neglected and are missing feathers (a common occurrence on factory farms), then you especially want a high protein content to help them regrow their feathers. Scratch is mostly corn, which isn't high in protein and they fill up on it like kids eating cake and ignore the nutritious stuff, so it's good to keep the scratch to a minimum.
For variety and added nutrition, Farm Sanctuary gives chopped up produce to their chickens, as well as mashed up hard-boiled eggs with the shells, up to one a day for each chicken but usually less. We do this, too. The eggs are high in protein, which is good. But, especially with layer hens who have been breed to produce far more eggs than is natural, the shells are needed to replace the huge amount of calcium they're using to create them in the first place. If calcium isn't supplemented for these high-producing layer hens, their bones weaken and they have trouble walking.
Farm Sanctuary also adds a bit of wheat germ oil that's vitamin fortified, for extra calories and fat. We don't do this because our chickens didn't come from commercial farms; those chickens have trouble keeping on weight.
One thing to help really skinny chickens is to not only give them egg but to also give them Exact (which is formula for baby birds) plus water.
What we feed our chickens: Our chickens get a crumble pellet. They pretty much get as much as they want to eat because they aren't in much danger of getting too fat, unlike turkeys. They get the crumble pellet spread around four trays so everybody gets access first thing in the morning and then about an hour before bedtime. We mix a little scratch in with the crumble. Also in the morning, they get chopped-up lettuce (they prefer romaine hearts), chopped-uptomatoes, mashed hard-boiled eggs with the shells, and cooked pinto beans (we crockpot them to keep the cost down). When in season, they get grapes, cut in half, too. Watermelon is a treat they love in the summer; we just set out a half or quarter and they peck it down to the rind.