I baked some cookies and did not realize the flour might have been too old. It has been stored in my canister on the counter. Can rancid flour make anyone sick?
How "old" are we talking about?
If the flour was white all purpose flour, was stocked in an airtight container, and your house gets not too hot in the summer I doubt the flour could have gone rancid. Rancidity is the deterioration of fats, and in wheat only the germ contains fat; white flour has been stripped off of wheat germ and therefore is very unlikely that it becomes rancid (anyway rancid flour is unlikely to make you sick)
Most flour deterioration comes from pests like meal moths, but you cannot miss them.
Nevertheless, if the cookies smell and/or taste bad you should throw them
Flour goes rancid primarily from the small amounts of fats present. At best rancid flour will contaminate the taste of anything you make with it. Worst case someone could experience a reaction from toxins introduced by different strains of bacteria.