Duck and Chicken are a little different in preparation and cooking. For both, one thing I like to do is loosen the skin over the breast and add some flavor, if just a few herbs or spices, salt and lemon slices.
For Duck, I prefer to dip or ladle very hot water over the skin a few times, it helps tighten the skin. I will then allow it to air dry, either by hanging, or as SanDiegoBBQ does, place it in the fridge to dry up. This increases the chance of getting a nice crispy skin. Then into a hot cooker until mahogany colored and crispy.
For chicken, I like to truss it up tight, I am less of a fan of spatchcocking unless time is a factor. I also consider splitting to yield a different result that spatchcocking. I prefer whole, trussed up tight so that all body cavities are closed off. No stuffing and no loose appendages. Brine in this manner or brine prior to trussing, doesn't matter.
You can cook it hot, 350F or even higher, or you can cook at 225F to 250F and run a longer cook. It will be closer to 4 hours at these temperatures and the skin gets moist and tender, not crispy. A totally different product. If I don't brine, I go very hot, 400F and offset heat, otherwise it dries unfavorably.