Since I started using f.lux all day (not just at night) several years ago those headaches have a been a thing of the past - it basically doesn't happen anymore.
I know f.lux is intended to be used in dark environments but since I rarely do color-sensitive work and prefer the lush, warmer color temperature (3800K for me), I see no reason to change my all-day use.
Anecdotally, Flux + Night Shift dramatically improved my longstanding insomnia. But that's just my anecdotal experience
However, I ask because I did try it for several months, and did not notice any effect other than the minor irritation of having to keep turning it off when I wanted to watch a film in the evening (and the constant malfunctioning of f.lux – although hopefully those issues would not be present in Night Shift).
I'm not sure I would be able to detect an improvement even if there is one though - there's too many confounding factors. So I'd like to see some evidence so I can make an informed decision.
But honestly, I use it because I like it, not for any positive effects it may have on my sleep. It just makes it more pleasant to look at screens after nightfall. Also, seeing the screen change is a very pleasant "hey, stop looking at Twitter/HN and go to bed!" reminder.
[0] https://en.wikipedia.org/wiki/Intrinsically_photosensitive_r... nal_ganglion_cells
A PNAS article about the use of e-Readers is often cited [0]. However, this compares a light emitting device to a book, and it's not clear how applicable it is to Night Shift vs. not Night Shift.
There is some research about the affects of light at different wavelengths on the human sleep cycle but I'm wary about using that as evidence for the efficacy of something like f.lux or Night Shift without specific studies done on their use in practice.
[0] http://www.pnas.org/content/112/4/1232.full.html