Kelvin isn't unique to f.lux. It's just the color temperature of light. It's a standard measurement. You'll see things like "2700K" on light bulb packaging. That's 2700 degrees Kelvin. It can be any number, like 4100K on fluorescent tubes, or 5000K for Daylight bulbs. Y'know? I'm sure you've seen this.
So, there is no answer here. The color temperature that you're exposed to at ANY TIME regardless of where you are or what you're doing always depends on the color temperature of the light source(s) around you, including the sun. Anything that emits light has a color temperature.
So there is no color temperature that's associated with the monitor off and with the monitor on and f.lux in use. "F.lux in use" isn't just one color temperature either. F.lux has a huge range of color temperatures that you can set. So, "f.lux in use" can mean any of its available color temperatures.
It doesn't end there: you also have to factor in the color accuracy of your monitor (which you have minimal control over) AND the way you have the color configured from within the operating system itself. So, any specific color temperature that you're using could be quite different for other people because of the monitor you have (I'm not judging your monitor, I'm just making factual statements). F.lux itself is accurate, but the actual color temperature that you see and are exposed to won't be 100% accurate due to all of these variables. This is ok though: we don't have to worry about it. As long as we're not being exposed to alerting light (blue light, especially bright blue light), it's fine. The number in degrees Kelvin is just for your information only. It's almost ambiguous. Don't set it and then say, "Ok, so that's precisely what that color temperature looks like" because that likely won't be true. All we have to worry about is whether we're getting the desired effect out of f.lux.
There's also the fact that even when f.lux is set to a certain color temperature and even if your monitor's color accuracy is somehow absolutely perfect (like, so perfect that it's absolutely 100% true to life), you still have to consider the color temperature of the light in your room. F.lux is really an assistant to help make it easier for you to avoid blue light. It can't do that by itself. If you're already doing a perfect job of avoiding blue light in your home but your computer is still emitting blue light, then that's where f.lux comes in. Start f.lux, filter out the blue light until it feels right, and you're done.
So, it's impossible to answer these questions. What's more is, I'd rather just advise that you relax and enjoy the added benefits of f.lux to your life because without f.lux, you'd be unable to use your computer near bedtime without being blasted by alerting/stimulating light.
