Actually, Red Pete took the words from a Russian novel he had recently read, "And Quiet Flows the Don" and took the melody from an Irish tune, "Johnson Says He'll Load More Hay". Pete was of course reading lots of Russian material in the 1950s.
Like all his commie friends, Pete made the transition from anti-war to pro-war in 1941, when the threat to his precious USSR switched from the US and Western Europe to Germany, but he switched back by 1946 after Germany was dead and anti-communism was again in vogue in our lands.
The song had nothing to do with Vietnam, since it was published in 1955, its original Soviet inspiration was a general "war is terrible" ripoff of All Quiet on the Western Front, the author, Mikhail Sholokhov, may actually been independently creating, in effect, "All Quiet on the Eastern Front".
Anyway, after the stalemate in Korea, OUR commies were really hot and bothered about undermining Western militaries but even more importantly, undermining patriotism and the idea of service, and "Where Have all the Flowers Gone" in 1955 is better understood in that light.
Of course, the Vietnam disaster was rocket fuel for their movement, but the song came before the first "adviser" stepped off the plane.
And now you know the rest of the story. Good day!
Thank you for adding that detail.