Hi Dietz! If you do a search for storing grain, you'll find lots of opinions and methods. I take the bag of grain, roll it shut, put it inside another plastic bag and close that, then put the whole thing in a plastic bin with a lid. I currently keep three bulk grains around, and stack the bins on top of each other in my brewery area.
If its kept dry and cool, unmilled grain will keep a long time - I've kept mine up to a year, but think it would stay good longer.