The present work investigates the mechanical integrity of multilayer films developed for flexible displays. The layers comprise tin-doped indium oxide (ITO) conductive coatings and alumina barrier coatings sputtered onto high temperature aromatic polyesters. The onset strain for tensile failure and related cohesive strength of the coatings, and their adhesion to the polymer substrate, are analyzed by means of bending tests and fragmentation tests. The former test enables accurate electrical resistivity measurements during bending of film specimens, and correlates the failure of the ITO coating to the abrupt increase of resistivity. In the fragmentation test, the progressive failure of the thin coating is examined in situ in an optical microscope as a function of tensile strain, with simultaneous measurement of the electrical resistance, for the ITO coatings. The results and their analysis enable to determine the influence of internal stresses and layer thickness on the failure mechanisms of the multilayer composite films, despite the occurrence of coupled failure processes between adjacent layers.