Does flaxseed oil need to be refrigerated

The only difference between regular whole wheat flour and white whole wheat flour is the variety of wheat from which it is ground. Regular whole wheat flour is ground from red wheat while white whole wheat is from a lighter pigmented wheat and thus the lighter color. In both cases the germ is still intact and thus as Jonathan Campbell stated, it will go rancid more quickly than white flour.

Keep it in a cool dark place and use up quickly if you can't refrigerate or freeze it.

When you keep it in the refrigerator or freezer and plan to use it for yeast breads, remember to allow it to warm to room temperature before using for best results with your yeast.

I think the Kadoya brand you bought was toasted as well, it just didn't bother to mention it. Everything I've bought from Kadoya has been toasted. They are easy to tell apart. Non-toasted is about the same color as say safflower oil, toasted is rather dark brown. Toasted is used primarily for finishing dishes, as a final flavor. A little goes a long way. Non-toasted is a pretty marginalized product; you see it at health food stores some times. I can't think of any culinary reason to prefer it over the many other choices and it is quite expensive. Maybe some folks have particular health reasons for choosing it.