Understanding aeroelastic issues related to isolators is pivotal for the structural design and flow control of scramjets. However, research on fluid–structure interactions (FSIs) between thin-walled structures and the isolator flow remains limited. This study delves into the FSIs between thin-walled panels and the isolator flow, as characterized by an oblique shock train, by quantitatively analyzing 11 flow parameters assessing the structural response, separation zones, shock structures, flow symmetry, and performance. The results reveal that an FSI triggers panel flutter under oblique shock train conditions, with the panel shapes exhibiting a combination of first- and second-mode responses, peaking at 0.75 of the panel length. Compared to rigid wall conditions, isolators with a flexible panel at the bottom wall experience downstream movement of the separation zones and shock structures, reduced flow symmetry, and minor changes in performance. Transient fluctuations occur due to the panel flutter. Two flexible panels at the top and bottom walls have a comparatively lesser influence on the averaged parameters but exhibit more violent transient fluctuations. Furthermore, the FSI effects under oblique shock train conditions are contrasted with those under normal shock train conditions. The flutter response under normal shock train conditions is more pronounced, with a larger amplitude and higher frequency, driven by the heightened participation of the first-mode response. The effects of FSIs under normal shock train conditions on the averaged parameters are the opposite (with a larger influence) to those under oblique shock train conditions, with significantly more drastic transient fluctuations. Overall, this study sheds light on the complex and substantial influence of FSIs on the isolator flow, emphasizing the necessity of considering FSIs in future isolator design and development endeavors.