Do you know if the by product of making beer has waste that could be used for chickens? I might look into that.
I think beer does have some wet grain as a byproduct.
Chickens can probably eat it, and it would be a source of energy (calories), but I do not know how much of their other needs it would provide. At a guess, it is probably quite low in protein, the protein it does have is probably not properly balanced, and it is probably missing several important vitamins and minerals.
If it is cheap, and you do some research, you might be able to use it as part of the chickens' diet. You would have to provide other things that balance it nutritionally, and I do not know what those things are or how expensive they are.
I planted some potatoes but they didn't develop.
I think potatoes need to be cooked if you want the chickens to get much food value from them. If the potatoes do not grow anyway, that does not matter. But if you try again, it's something to keep in mind. Cooking large amounts of potatoes might be inconvenient, and might get expensive too.
I know that beans need cooking before feeding them to chickens. (You did not mention beans, I'm just thinking of things that need special treatment before feeding.)
Carrots are safe to feed raw, but chickens eat them much better cooked. I think the same is true for many other vegetables with similar textures (turnips, beets, etc.)
I would just like to supplement my feed not replace or stop buying commercial feed.
Even as a supplement, you need to pay some attention to the right balance of nutrients.
For example, if you offer lots of low-protein supplements, the chickens might eat them and end up short of protein. (Gamebird Starter or Turkey Starter tends to be high in protein, so it can help balance out some low-protein supplements. Check the cost, of course, but it often costs about the same as the chicken feeds with less protein.)
Even if you provide the right balance of protein and energy, they still need that protein to contain the right balance of amino acids, and they need the right amount of certain vitamins and minerals.
Chickens will often stay alive on a not-quite-right diet, but they will tend to grow slower and lay fewer eggs. Sometimes that is still worth doing, if the other things you offer are so much cheaper that you still come out ahead. But it is definitely something to consider. Feeding only a purchased complete feed is usually the best way to get the best growth from meat birds, and the most eggs from laying hens.
I am in the chicken business, I don't have just a few birds. There is a mill in driving distance but after calculating driving there is no cost savings, plus being in a humid state I like my feed fresh. Too much at a time will go moldy.
Not being able to store the food for long is definitely a consideration.
I assume you already calculated how long you can store it, and how much feed you could buy at a time? If you buy it freshly milled, you might be able to store it a little longer than if you buy it at the feed store (because it gets stored on their shelves too.)