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Flu vaccines (the flu shot and the nasal-spray flu vaccine (LAIV)) cause antibodies to develop in the body about two weeks after vaccination. These antibodies provide protection against infection with the viruses that are in the vaccine.
The seasonal flu vaccine protects against three influenza viruses that research indicates will be most common during the upcoming season. Three kinds of influenza viruses commonly circulate among people today: influenza B viruses, influenza A (H1N1) viruses, and influenza A (H3N2) viruses. Each year, one flu virus of each kind is used to produce seasonal influenza vaccine.

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About 2 weeks, if you get the flu after the shot it just means you had it to begin with......

Well, I know for one thing that the flu shot is only effective if they choose the correct flu strain to protect against, so it might or might not even work.