The way people treat their country's flag is often seen as a measure of their patriotism, or lack thereof. And that's also why, once upon a time, armies used to carry their flags with them into battle: it was a symbol of what they were fighting for, and it was patriotic to die for it. "War Is Kind," however, chucks that whole idea right out the window. The flag in stanza 2, for example, is "unexplained." In addition, there's nothing really patriotic about the war; the soldiers don't appear to be fighting for anything in particular. After all, they were simply born to do this.
This poem makes patriotism seem cruel and pointless, since these soldiers were born to die anyway.
The colors on the flag in stanza 4 suggest that patriotism is closely related to death, because they evoke blood and sickness.