This order of operations is incorrect, though the grandparent set you up a bit by saying "released on iOS". In order to install the f.lux app you would first need to be jailbroken, ie able to run pirated apps.
Apple's concern was that f.lux changes the color of the screen outside the app, and that fact alone goes directly against Apple's philosophy of keeping apps in their own respective sandboxes. Only Apple is allowed to change UI outside of an app. Consistency at all costs.