By its nature, the functionality of their app breaks the app sandbox, currently via unsupported APIs. It is unclear whether Apple wants to ever support the functionality required to make f.lux run. My guess would be no, because it would be difficult/impossible to design without also allowing malicious behavior, and Apple is understandably keen to keep the App Store's reputation as a trusted and harm-free source of software.

In addition, I imagine other app developers might not be happy with a sanctioned means to mess with the running of their app: more interactions means more to test and less control over the user experience.

More likely is that this functionality will be incorporated into iOS itself in a future update. But it still runs the risk of Apple considering it aesthetically distastefuland thus never doing it.

Monitors are not perfectly calibrated, so if you send one a raw sRBG image, the result will look subtly wrong. To fix this we have monitor profiles (mappings from sRGB colors to the values needed to accurately display said colors on a particular monitor) and CLUTs (color look-up table, a table that the graphics chipset uses to perform said transformation on the fly as it synthesizes the video signal. It was implemented in analog video signals with RAMDACs, now with digital signals we don't need the "DAC" part, but you get the idea).

What f.lux does is (ab)use the CLUT to change the color temperature of the video signal sent to your monitor, cheaply and without requiring any modification to existing software. This is great if you trust f.lux, however clearly Apple cannot trust random apps with persistent access to the CLUT, because people could use it to do things like, say, completely blacken the screen.

f.lux wants to modify how the screen appears when other apps are running.

In general, this is not the sort of thing you want sandboxed applications to be doing. You can imagine the problems that a bad actor could create with this capability.

Because the APIs they need are not approved by the platform owner.

f.lux needs to be able to control the screen at a very low level while other applications are running, which isn't possible using just the public iOS API. The sideloaded version of f.lux used some internal APIs to do that, which wouldn't fly if they submitted it to the App Store.