Tameria, my understanding was that there was only one version of the vaccine each year. ( per hemisphere )
Unless that means that the shot in August is actually the one from the previous year. In that case, it would make no sense to require flu vaccines at the beginning of the school year.
This problem could be easily worked around, of course by changing the deadline to later in the school year. Or by having the schools supply the vaccines themselves. Both school districts I have been involved with locally have offered free flu vaccines seasonally.
In my experience, the uptake is about a third of parents who will sign off for their children to get the shot in school. Others, especially the ones with health insurance, will get theirs on their own.