The class of high-altitude long-endurance aircraft often has very slender wings with minimal structure. This leads to large trim deflections and coupling between the vehicle flight dynamics and wing vibrations. When this coupled behavior becomes unstable, it is referred to as body-freedom flutter. Body-freedom flutter behavior is dependent on the inertial and constitutive properties of the wing, as well as the fuselage. This relationship is explored for an aircraft representative of the Horten IV flying wing, using an efficient yet rigorous analysis that relies on geometrically exact, fully intrinsic beam equations and a finite-state induced flow model, which is implemented in the computer code NATASHA (which stands for nonlinear aeroelastic trim and stability of high-altitude long-endurance aircraft). The wing inertial and stiffness properties were calculated using a realistic representative section using the section analysis tool called variational asymptotic beam section analysis. Trade studies on the body-freedom flutter behavior were performed by varying the fuselage properties and the internal wing structure, as well as examining the effects on the flutter speed, flutter frequency, and flutter mode shape.