Gotham is referred to as a timeless series, so they can't be referring to a specific war we know of. Such examples of references to the war is where Captain Barnes talks about the war he was in when explaining to Gordon about 'the line'.
Haven't you just answered your own question: it can't be in reference to a particular war due to the timeless nature of the series, so it instead refers to some unspecified past war?
Given the technological time frame of Gotham, the story has to have happened in the last 50-60 years in the US; and there has been no shortage of past wars in this timeframe. Even if you expand it to 100 years, you'll still find that there will always have been a recent past war.