Flexible aeroshells, featuring deformable membrane surfaces supported by pressurized gas, offer a novel re-entry system for high-altitude deceleration during re-entry. The flexibility of structural components introduces unique challenges in predicting aerodynamic behavior, as deformations can significantly alter the flow field, affecting pressure distribution and potentially causing aerodynamic instabilities. Therefore, coupled analysis is crucial to ensure the performance reliability of inflatable aeroshells. This study investigates the unsteady aerodynamic behavior, considering structural deformation in a two-way partitioned coupled manner in transonic flow. The dominant deformation patterns are identified using dynamic mode decomposition and the greedy compressive sensing algorithm. The findings reveal that the primary deformation pattern combines axial deformation and swing oscillation. The dominant oscillation frequencies remain different from the eigenfrequencies, indicating that the aerodynamic force is the primary driving force of such oscillations. The time evolution of these dominant modes indicates purely oscillatory behavior rather than increasing or decreasing trends. These insights are critical for the design and reliability assessment of inflatable aeroshells in varying aerodynamic environments.