I'm not sure I understand the question 100%, but here's how to use f.lux for sleep:
Set f.lux to a very warm color temperature (as warm as you can tolerate - I use 1200K) an hour or two or three before going to sleep (if you need assistance with setting f.lux to a super warm color temperature after sunrise, then I can help with that because I have to do it nearly every other day) You should also lower your monitor's brightness as much as you can tolerate during this time too. I set mine to about 10%, but I sometimes set it to 0%. Sometimes I even simply turn my computer off and do almost nothing in complete silence for an hour or so before going to sleep. It's like meditation, but with no specific focus on anything in particular, unless that's needed. The mind loves that freedom, so try it out if you're curious! It's a little bit like how you do your best thinking in the shower or on the toilet or whenever you're doing any other sort of mindless activity - but BETTER.
Getting back to the color temperature and brightness, that's only a part of what a person should do. You should also do the same thing with ALL light sources in your home, including things like your T.V. and mobile devices, etc. You see, f.lux simply makes it possible to use your computer before bed without being blasted by blue light. The problem with our modern world is, most light bulbs and T.V.s and mobile devices still blast us with too much blue light - and it's usually always WAY too bright to be using them before bed (only, the vast majority of people aren't aware of it). You also have to consider the brightness of these light sources.
So, let's say you are able to make all of your light sources produce a nice low-brightness super-warm color temperature and you are able to avoid watching the T.V.. Well that's great, but what about the computer? It's still going to be producing lots of blue light. That's where f.lux comes in. In today's world, most people use their computers right up to the last second before going to sleep. I do. So, I have f.lux.
Why is the brightness important? Think about a full moon for a moment. The sunlight that it's reflecting at us isn't a warm color at all, but it's not bright enough to really affect us even though its invisible energy is enough to affect us (that's a part of what makes sunlight energizing - it's not just the visible light). So, the brightness of all light sources needs to be lowered as much as you can tolerate, even if some of those light sources are fairly blue. After all, f.lux isn't a magic bullet.
Sound levels are important too because loud sounds can be just as "alerting" as bright blue light - sometimes even more alerting. So when I'm in that last hour or two (or three) before bed, I make sure I become quiet and I reduce the volume on my computer a lot too. I close doors quietly, I set the toilet lid/seat down quietly, I do everything quieter. It really makes a difference.
Of course, there's still more to consider, like the pace at which we do everything that we're doing in that last hour or two before bed. I mean, if we're rushing around trying to get ready for bed as quickly as possible, then of course falling asleep will be difficult. If we instead move slower and calmer (walk slower too) and practically pretend like we're super tired and can't move any faster than a snail, then falling asleep will naturally be easier.
Some people find that they lie awake for an annoyingly long time because can't stop thinking about the next day's agenda or To-Do List. The best solution to that is to physically write everything down using a real pen or a pencil and real paper, and put it somewhere near your bed where it's going to be extremely easy to review it when you wake up. The physical activity of actually writing it all down puts your mind at ease because then you can rest knowing that you can simply look at it when you wake up. Simply typing it into a computer isn't enough unfortunately because writing is more physical than typing. It's much easier for the brain to remember that you did it.
So yeah, f.lux is just a very small part of the big picture.