Is it possible to be immune to the flu?

Yes & no: You probably develop good cross protective antibodies to some of the common flu strains. However, the flu tends to mutate some every season & if the strain you are exposed to has changed enough you will never be immune to it. Somewhat like kids dressing up in costume, every season they change their costume & may not be recognized.

Yes!: It's easy....You just get a flu shot. The "natural way" is more difficult. You do develop immunity to the flu after you recover from it. The problem is that next year's strain will be completely different, so it won't do you any good. Over the years, there can be some overlap, so people previously exposed may have partial immunity, but it's a lot easier to just get vaccinated.