I save and use dryer lint to light kindling in our wood stove. You are correct, it would be good for a flint strike start as well, assuming it is kept dry.

For storage we typically use an old detergent pod container to store the lint, that way you can close the lid and it stays contained.

Save your dryer lint and set it aside in a plastic bag, it is an amazing fire starter. If you are using firesteel it is the ideal thing to have on hand rather than buying starters or searching for dry grass and such.