Flexible systems that can conform to any shape are desirable for wearable applications. Over the past decade, there have been tremendous advances in the domain of flexible electronics which enabled printing of devices, such as sensors on a flexible substrate. Despite these advances, pure flexible electronics systems are limited by poor performance and large feature sizes. Flexible hybrid electronics (FHE) is an emerging technology which addresses these issues by integrating high performance rigid integrated circuits and flexible devices. Yet, there are no system-level design flows and algorithms for the design of FHE systems. To this end, this paper presents a multi-objective design algorithm to implement a target application optimally using a library of rigid and flexible components. Our algorithm produces a set of Pareto frontiers that optimize the physical flexibility, energy per operation and area metrics. Simulation studies show a 32x range in area and 4x range in flexibility across the set of Pareto-optimal design points.