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Hey, this might not be any help, but I thought I'd post to bump your thread as I was trying to achieve something similar.
I'm using a Google nexus 5 and whenever I try and use the phone's own invert colours toggle, either flux turns off, or the colour invert turns off in a conflict between the two.
It would be great if there was a way to have both on at once. I had just been using flux's Darkroom mode all the time which turns everything greyscale, then inverts colours, then the colour temperature to red, which is not quite an ideal solution.
What OS are you using? I stopped using flux because lucky for me lineageOS has a settings menu called live display where you can set the screen's colour temperature same as in flux. That plays nice with the invert colours and greyscale settings, as all of them run through the OS and don't compete for priority.
If I hadn't found that I'd still be in the same boat though.
