You might find this interesting. We ate some of our rotation stock this week, with varying results. All of the food was at least ten years old or older.
The white flour and salt we ate (tried to eat) is the only food I have ever stored straight in the bucket without oxygen absorber or even a desiccant. This flour had definitely gone off, no doubt about it. We tried to make sugar cookies with it, the result was inedible. It has a sour, sodium taste and a faintly disagreeable odor. I knew it had gone off but wanted to see as an experiment if flour remained edible even when it acquired the wrong appearance and smell. I thought baking it might "sterilize" it sufficiently.
The sugar cookies were horrible and had to be thrown out. The white flour without an oxygen absorber was a loss, probably at six years if that. It had been stored in a variety of less than optimal conditions but I imagine even if stored in a perfect environment it would have been stale unless an oxy absorber was used.
The salt has also acquired a slightly funny smell but I honestly believe that it is otherwise perfectly fine, a decade after being put in a bucket and the lid closed. Salt almost takes care of itself, but obviously any precautions you take in storing it are still a good thing.
The oats were fantastic and tasted as fresh as the day we bought them. They had been stored in a bucket in a mylar bag sealed with desiccants, but no O2 absorber. I believe more than 160 pounds of oats survived eleven years with no major degeneration. Brown sugar on oats is survival food. There's enough nutrition and calories there to keep most people going for a long time on that kind of diet.
The canned peaches were twelve years old and were perfect. The only detail I would point out here is that the syrup they were stored in was fairly thin, like water almost. Some brands have the syrup so thick and slushy it is almost like jello. I can only imagine what a sweet, nourishing treat that peaches would be in a long term shelter environment. Just make sure you know the brand, have tried it and can be certain the syrup is thin to avoid fungal growth in the can.
If you mix the oats with brown sugar and some dried bananas and chopped peaches, that's enough calories you better have an exercise bike generator in the shelter or you could get pretty robust eating that for breakfast each day.