Making your own feed is typically more expensive than buying feed, if you want to actually meet the needs of the chickens. The cheapest ingredients tend to be deficient in some way, or else be things that chickens do not digest.
I would start by making sure feed is not being wasted (spilled on the ground, eaten by wild animals, etc.) Buying feed for your birds to eat is good, but buying feed they do not eat is wasteful.
The next obvious way to reduce food costs is to reduce how many chickens you have (eat them, sell them, give them away.) Think about why you have chickens, and why you have each particular chicken, and decide if any can go.
Depending on how much food they are eating, you may be able to save money by buying the food in bulk (like a whole pallet full at once), or buying directly from a feed mill rather than from a store that has it neatly bagged.
You certainly can offer them other things to eat, like table scraps and vegetable trimmings, and they will balance their own diet (within reason, limited by what is available to them.) That can reduce how much of the purchased feed they eat. But for a large flock, it will not make very much difference unless you have a large area for them range in, or you bring home large amounts of other food.
Chickens like to scratch through compost piles and eat bugs & worms, so if you have a compost pile, letting the chickens have access to it can help a little on the feed bill too.
I've read of people who bring home large amounts of food waste from restaurants or grocery stores. They let the chickens eat what the chickens want, compost the rest, and let the chickens pick through the compost too. It apparently works for them, but I don't know the details. For many people, the work of doing that is more than the work of doing something else to earn money to buy chicken food. (Different things are best for different people, so I can't say what is "best" for you.)
I recently saw a tick tock or some similar video on someone taking hay and an egg and making their own pelleted feed.
If you have more eggs than you need, you might try selling the extras. Using that money to buy chicken food is probably a better financial choice than feeding the eggs directly to the chickens.
Hay is very bulky. Yes, chickens can eat some hay. But they are not able to eat ENOUGH hay each day to get the nutrients they need, even if the hay did contain all the right nutrients (it doesn't.)
Edit to add: you can sometimes save money by buying a "different" chicken food. The chickens do not care whether the label says chick starter, grower, layer, all-flock, flock-raiser, feather-fixer, game bird starter, duck chow, or something of the sort. If it has about the right amount of protein, and is based on grains & soy, it is probably fine to feed to the chickens. Do check the calcium level-- layer has too much calcium for young chicks, and laying hens need a separate source of calcium if they are eating foods that are not labeled "layer." But oyster shell is fairly cheap and does not go bad, so you can sometimes save money by putting out a dish of oyster shell and feeding whichever suitable feed is cheapest each time you buy. (But watch the bag sizes, and be sure you are comparing same-size bags or price-per-pound. You don't want to get tricked by smaller bags.)