How do I kill mold in a cooler?

Scrub out loose gunk with dish soap and water, then mix 1 tablespoon bleach per quart of water (or 1/4 cup per gallon). Swish that around, let it sit for 15 minutes, then rinse thoroughly. Let the cooler air dry completely with the lid open before storing again. Bleach kills the spores reliably — vinegar only handles surface mildew.