This paper concerns an important application of the (123)-avoiding class of Aunu Permutation studied by earlier by Usman, Magami and Garba under various topics such as enumeration, thin cyclic desighn and association schemes. .In this report, some method of construction are used using accents and descents as enumerated by positive and negative units in a manner that resembles, in some sense, the Motzkin numbers. This method produced some graph models which when superimposed produced the required design of a slanted flag. This paper therefore uncovers yet another rich property of this class of permutation pattern: applications in design theory which interested researchers can further explore.