I've been using f.lux for I think about a year. Honestly I think it's just a placebo and I haven't noticed any real effect. My sleep schedule is terrible. I just feel I should comment because all of the only people commenting are those that did benefit (or at least believe they did.) The comments are not an accurate survey of how many people really did see an effect.
The normal, medical wisdom is "don't look at a screen before you need to sleep". F.lux is proposed as a way to ameliorate the effects of our reckless geeky disregard for what sleep scientists are telling us to do.
If you have trouble sleeping even without the interference of electronic screens or lights, F.lux isn't going to fix any of that because you don't have the problem it addresses.
The point isn't that it puts you to sleep like a drug. The point is you are ready to sleep; you don't spend forever falling asleep, that sort of thing. So setting a reasonable sleep schedule is still up to you.
I get that. I certainly didn't expect it to solve all my problems. I am saying that I don't think it had any effect for me, or at least that it was very small.