Coupling between the strain gradient and the electric polarization, also named flexoelectricity, is a fundamental but often overlooked property in solid dielectrics. The past ten years has witnessed its great potential in sensing and actuating applications, especially in nanomaterials or nanostructures. The recently discovered giant flexoelectricity in barium strontium titanate (BST) perovskite above its Curie temperature has boosted the research interests on flexoelectricity to a new height. The possible interpretation of the enhanced flexoelectricity in BST was initially attributed to the non-crystalline polar-phases or polar nano-regions existing in the perovskites, then to the inner micro strain generated from the material densification process. In this paper, we analyzed the origin of flexoelectricity in this kind of materials by using both analytical mechanics method and finite element simulation method. Our results suggested the inner micro defect generated during the material densification process would weaken the flexoelectricity of the materials. The observed polarization in the studied materials was likely induced by other mechanisms rather than the pure flexoelectricity.