Does it ever explicitly say that in the show? In 'The Great Hazzard Hijack', they say that Phil Ackley is "the one that saved Luke's life during the war", but I don't think Vietnam is ever mentioned.
We know approximately how old Bo and Luke are....supposed to be, mid 20's, I mean come on! They're out of high school, not old enough to be grandparents but still old enough work, be on their own etc. and still young enough to jump across cars, fight in bars etc., so The Korean war was in the '50's...they'd need to be late teens early 20's to be in the Korean war, so they'd be born in the 30's to be in Korea. They would've been in their 40's during TDOH times and so the only other war Luke COULD have been in was Vietnam!