Usually we did trim in a semi gloss, not high gloss. Yes you can paint the ceiling the same as the trim and the sheen will help it show, but it won't be as standout as it would if you painted the ceiling a different color. You might consider a color between the white and the flax for the ceiling to give a brighter look and yet have the trim stand out. Especially with such high ceilings, you certainly can add a little color.

Given the warmth of the flax, I would go with an off white, though a stark white can work with that too. What other colors or finishes are there? If you're going with more of a nickel finish, then the white would be better, but if you're going with a warmer antique brass than the off white would be better.

Thanks Annie! Just got home after making the final choices and didn't see your response until now. Here is what I did. Flax flat,for the walls. Sherwin williams Pure White,which actually has a tint of Raw Amber in it for the trim and all wood work which is substantial. Raw Amber is SW's brown. And 75% flax and 25% white on, the ceilings! flat.

Thanks again. I'll post pictures of the house soon.