Afaik dry eyes aren't caused by blue light, just by prolonged staring at the screen with less-frequent blinking. The strain, to my knowledge, is mostly from keeping the eyes focused at the same rather close distance in front of you (the eye-moving muscles get sorta cramped). So the main solution to both is to take frequent breaks, go away from the computer and look at objects further away. Plus some exercise for the muscles helps—moving the eyes in circles and side to side, and focusing far/near in turns.
However, Flux might help in that if you aren't kept as energetic at night by the blue light, you probably won't sit at the computer as long. There's sometimes a sort of a hyperactive state when you deal with stuff, browse the web or whatever, and where you don't want to go away for an hour or two straight—but of course that's not good for the eyes, and Flux might help avoid that.
