Does skin break out from being too dry? Yes. Well, for me it does. I don't use a moisturizer, however I do make sure I drink enough water (at least 2 liters per day) and every other day I use olive oil to wash/moisturize my face...I wash my face, then I use olive oil to hydrate my skin...I rub it in for about 3 minutes, and gently rinse off with the aid of a washcloth, if I need it...You will have a bit of olive oil left on your skin, but your skin will soak that up...I also use a toner afterwards (I alternate between sea salt + water and apple cider vinegar diluted with water).
Edit: Forgot about the original question! lol.
I haven't tried flaxseed yet, but I've been meaning to pick some up the next time I'm at the store. I've been reading good stuff about it, and hey, it can't hurt to try! Even if it doesn't help with acne (not saying it won't, just "if"), it's at least beneficial for your overall health.