According to the Centers for Disease Control (CDC), you should allow two weeks after getting a flu shot to develop protection against the flu. That's because after vaccination, the body
has to work for a while to create the protective antibodies to the flu virus.
Bear in mind, though, that there's a lot of variation in how fast different people's immune systems work. Many people will develop antibodies sooner. One research study found that among healthy adults, a majority had developed protective antibodies by the seventh day. On the other hand, the elderly and chronically ill often take longer to develop an immune response, and some never do. Still, even in a less-healthy group, one study found that many of them had developed protective antibodies by the tenth day.
The bottom line is that your best chance at being protected by the flu vaccine is to get vaccinated as early as possible. But later is better than never. Even if your body has only partially developed antibodies when you encounter the actual influenza virus, that little bit of a head start could mean your influenza bout is milder, or that it gets better faster.