1) Store feed in something chew-proof - steel cans
2) feed the chickens via treadle feeders. I have the Rat-Proof Chicken Feeders and I haven't heard about any that have better features yet, these have a cat-door-type opening which I prefer, not the guillotine style. Also holds a lot, enough for my needs, and there's not much spilled feed. The new models are better than the older model (I have one of each)
https://ratproofchickenfeeder.com/Medium-Ratproof-Chicken-Feeder_p_1.html
@RoyalChick just got a couple this Fall. I know the chickens there have learned it, but I don't recall reading whether RC listed the pros and cons and what they do or don't like about it.
I actually need to train the new Buckeyes on my second one, they've been eating out of the regular chick-then-pullet feeders and I've been so busy with this crazy stupid run roof build I've not trained them yet. I also haven't wanted to stress them along with construction going on (though they are pretty chill with power tools); Shehnai is a growing boy and crazy with hormones and I want to take the time to actively train them and not have him especially feel at all insecure about getting enough to eat.
Mice find open feeders in wintertime here. When I watched a mouse go in and out I researched the feeders out there, and when I switched to the treadle feeder I was surprised how more slowly "they" went through their feed. The mice were taking a lot!