Flexoelectricity offers promising opportunities for next-generation miniaturized electromechanical devices. While this electromechanical coupling effect exists in all dielectric materials, it is most pronounced in nanoscale soft materials capable of large deformations. Despite the prevalence of structural contact in flexoelectric applications, theoretical frameworks for analyzing flexoelectric contact mechanics remain largely unexplored. In this work, we present a comprehensive theoretical framework for contact mechanics in finite deformation flexoelectricity, using isogeometric analysis to model both mechanical and electrical contact constraints effectively. The integration of isogeometric analysis allows for precise geometrical representation and higher-order continuity, making it particularly suitable for capturing the complex interactions in flexoelectric contact problems. We validate our framework through two case studies—insulator-dielectric and conductor-dielectric contacts—demonstrated via a Hertzian contact problem and a radio frequency (RF) MEMS switch application.