I'm also having the same issue where f.lux doesn't work on my 2nd monitor.
The 2nd monitor's HDMI cable is connected to a USB display adapter that's plugged into a USB port on my laptop.
Adapter Name: MCT USB3.0 External Graphics Device
Driver Provider: Magic Control Technology Corp.
Driver Date: 6/20/2020
Driver Version: 1.4.2001.620
That would be great if you are able to fix it, thank you, Kurt