If I remember correctly, f.lux had an iOS app but they got removed from the store just prior to Apple announcing their own support for the same feature.
They do have an Android app as well as desktop apps. f.lux has been in the space for years and years now.
flux had an iOS app, but it was always side-loading through Xcode (or for jailbroken) but never on the actual iOS App Store. They need to use private APIs so it was never authorized in the first place.
If I recall correctly, they started with doing a screen overlay, and migrated to using the hardware gamma tables (I think I might have pointed them to it?). Android apps that do screen dimming use overlays, which ends up causing flickering.
They do have an Android app as well as desktop apps. f.lux has been in the space for years and years now.