Surprisingly, there isn't much known about it. Since the virus mutates so quickly, achieving long term immunity has never been a goal of the vaccine. There hasn't been much interest in studying how long immunity lasts since the virus likely changes before immunity wears off. It probably wouldn't be easy to get funding for such a study, because it doesn't have much clinical importance, although it would be interesting information to have. We only looked at it as a small part of a larger study, because it was important to know whether the 1976 shot was confounding our results.
There is quite a bit of individual variation, depending on age, health, presence of immunocompromising conditions, history of previous vaccines, etc. It's possible that in some people immunity wears off in months, and sometimes it's advised that you don't want to get the flu shot too early, because immunity might wane if influenza doesn't show up in your community for 6 months.
Bottom line is, we don't know how long it lasts. Months in some people, many years in others.