It is possible to still get the flu (strain covered by tye vaccination) until a immune response has been triggerred by the vaccination.
It is also possible that one catches the flu just before the vaccination is given.
It is also possible to get another flu, not covered by the vaccination, at any time. A vaccination does not cover all flu strains likely to be present, but usually only those strains likely to pose the most risk.
It is also possible a new high risk strain develops after the release of a vaccination...and such won't be covered by a vaccination. While this is possible, it is better to have immunity to known flu strains than not to have the flu shot assuming that it won't be effective.