If he's active duty Army, try firstnamelastname@usa.army.mil firstname.lastname@usa.army.mil. if it's a somewhat common name try adding .1 after the name and incrementing up if necessary.

As a General, he's likely in charge of some really big organization, like a whole military base or CCMD (combatant command). Try looking through the emails you get to see if you can find some context for where he might work, then search for an about page or contact page on the public web. You won't get him directly but someone who knows how to route the information up to him.