I've heard that some food joints would offer military discounts back when people were figuring out how bad Vietnam was especially with how many vets were coming back broken and homeless. Theres at least one place near me that's had a veterans discount as far back as '78, they also let folks camp out in their parking lot since it was a bit bigger to accommodate the firetrucks since they were in a more central location than the fire station at the time.

Rambling aside, veterans discount started out as a way to help conscripted veterans during and after the fustercluck that was Vietnam and then was hijacked at some point.