If you don't grind them up, your body can't digest the contents and they will pass out of your system undigested. Your body can't break down the fibrous coat and the only benefit you would get is the extra fiber. You could actually plant them after they pass through and grow a flax plant.

You have to break the shell to get to the fatty acids, but they degrade very rapidly after ground up. The seeds keep for a long time as long as you don't grind them.

Your best bet is to grind them up when you plan on consuming them, but only the amount you plan on consuming.

I good source on fatty acids is Udo Erasmus's book- Fats That Heal, Fats That Kill