Not about the flu shots but this is something to remember and publicize:
Wikipedia:
In 1993, Claude Hannoun, the leading expert on the Spanish flu at the Pasteur Institute, asserted the precursor virus was likely to have come from China and then mutated in the United States near Boston and from there spread to Brest, France, Europe’s battlefields, the rest of Europe, and the rest of the world, with ....
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The “experts” always want to involve the United States in the Spanish Flu propagation story, but I think there is a greater chance that the “Chinese Labour Corps” workers hired by the British to free up men for front-line duty might have played a role. I believe the French did likewise, too - and all late in the war.