The FAQ says "Unfortunately, you can only use f.lux today on displays that are directly connected to your computer." but this is not entirely correct.
On my system, F.lux manages the color of an external display that is driven as follows: mini-dvi port -> StarTech MDP2VGA -> monitor VGA port. Here are my details:
macOS High Sierra
MacBook Pro early 2015
Thanks for your great tool.