Answer:
Only one vaccination (for each type of flu) is needed as long as the virus does not mutate. They will have lifetime immunity* to the exact same virus in the vaccine after one immunization. If the virus mutates into a new form, then they will need a new vaccination for the new virus.
However, if your question is more about how many shots they need to create the initial immunity, then children under 10 need a series of two vaccinations. The second one is given approximately one month after the first and then in 3 - 4 weeks after the second one, they will have produced immunity for life to that exact virus strain and sometimes to very similar ones.
*Some vaccines eventually lose their ability to protect over time and that is a good reason to get a flu shot each year to be sure your protection is still working.