The Flying V is a flying wing aircraft consisting of two pressurised passenger cabins placed in a V shape. Its longitudinal and lateral control is ensured via elevons and split flaps on the outboard wing, and rudders on the tip-mounted winglets. The goal of this study is to devise a design for the outboard wing of the Flying V through a constrained aerodynamic shape optimisation at cruise conditions. The design process is divided into a geometry preparation phase in which the existing parametrisation is adjusted, followed by a planform design optimisation guided by the Differential Evolution algorithm making use of a vortex-lattice method and an Euler flow analysis. The cross-sectional shape of the wing is subsequently optimised through a Free-Form Deformation (FFD) shape optimisation based on the Euler equations. Two FFD optimisations are conducted to evaluate the effect of the integration of the elevons. The highest lift-to-drag ratio is obtained by neglecting the control surface integration and amounts to 20.3. While the constraints related to this elevon integration reduce the efficiency to 19.4. The overall efficiency gain compared to the original aircraft design is equivalent to 13% and 8%, respectively. A further increase is expected once the inefficient outboard wing is optimised in more detail.