What year does flowers for algernon take place?

It was wrote as a short story in 1959 and as a novel in 1966. The time could in both cases be regarded as "the near future". Such as when we have the intelligence enhancing procedure available.

The story is somewhat timeless, though. You could read it as early as 1940 and as late as now, and it wouldn't seem anachronistic.

The movie, on the other hand, is hopelessly dated, both in it's offbeat psychedelic montage "effects" and in showing a roomful of refrigerator-sized computers while doctors (and everyone else) chain smoked!