Is it inappropriate to get someone dog tags as a gift if they're in the military?

No, don't do that. He can't wear them so it wouldn't serve any purpose. Find a nicer anniversary gift, something that is between you both. Dog tags are a novelty to those who don't wear uniforms, but to those who do, well, they cannot wear them, they have to wear the ones issued to them, and second, it seems so impersonal - they are used to identify bodies, that's their purpose. I don't think that's a good anniversary present.