I've had serious problems with weevils in cornmeal put up WITH bay leaves.
Put it up with mylar and oxygen absorbers and I would think you could get 7-10 years. Do NOT let your cornmeal sit around for a while before you pack it though. Get it home and get it packed as soon as you can.
Even if frozen not more than a season or two. Grinding exposes the oil to air causing it to oxidize. Whole dry corn can last much longer. I put whole corn in plastic bottles then freeze to kill all bugs and eggs. Then thaw and put on a shelf.