Part of the problem here is that you're trying to start an application which needs to affect the screen.
An application started with task scheduler on start up will start before login, but it will not have any interactivity with the desktop/session, so you won't be able to see anything it does (particularly a problem for f.lux). This is also why you don't see it in the tray. Check task manager and you may see it.
There might not be any way for you get this to work on your own; it may require f.lux to be modified, but I'm on mobile so it's difficult for me too research it right now.