Doc,
A flatbow can be a selfbow and vice-versa. Either one can be backed with sinew or another natural material such as rawhide but it ceases to be a selfbow because of the backing. For a eastern Native American bow, hickory would be hard to beat as a wood. Osage Orange (Bois D'Arc) would also be good and, many would argue, better. As for length, use the formula of draw-length X 2 + 4" as a rule of thumb. In other words, if your draw length is 28" then that number times two is 56". Add 4" and you have 60" as a MINIMUM length of the bow. Please note that I said "minimum length". The bow can certainly be longer but any shorter and it will tend to stack and do various other bad things like take a set, etc. Generally speaking, any bow longer than you are tall will be difficult to deal with.
Hope this helps,
Storm