It would appear that Adobe do not offer any sort of Military or military Veteran discount.
I used the Adobe 'chat' to ask the question and was advised to call 'sales'.
I called sales and they couldn't answer my question, but said they would connect me with 'Customer Service'
Spoke to customer service who never really grasped what I was asking and after a long delay (after offering to reconnect me with sales!) I was given the standard web address for the software purchase page.
A great shame that it's possible to get a student or educational discount, but over 35 years of military service isn't acknowledged by Adobe.
If I recall correctly your Base or Post Exchange Software sales can tell you for sure. I've done a search on the Adobe site and there is no mention of anything like that.