Ive never had a flu shot. My view has always been to let my immune system fight it each year, and then to save the flu shots to when Im elderly. I dont know how true it is because Im not a doctor, but I read that if you always get flu shots your immune system weakens and when it does get hit with a bad bug, because it doesnt fight the flu full strength every year it becomes a struggle.
I personally wouldn't be happy with whoever gave your kids the shot without asking.