In this work, a novel multiscale topology optimization method has been proposed for the design of electromechanical energy harvesting systems converting mechanical vibrations into electric currents made of non-piezoelectric materials. At the microscopic scale, the material is assumed to be periodic, porous and flexoelectric, although not piezoelectric. A first step of topology optimization is performed, in order to maximize the effective (homogenized) flexoelectric properties of the material, where a flexoelectric homogenization model is first formulated. As a result, the effective material, although made of a non-piezoelectric material, has apparent piezoelectric properties. In a second step, these properties are used to model the behaviour of a dynamic electromechanical energy harvesting system structure. A second topology optimization step, this time performed at the structural scale, aims to maximize the system Electromechanical Coupling Factor (ECF) for a given forced vibration frequency, including the micro-inertial effect. At both scales, an Isogeometric Analysis (IGA) method is employed to solve the strain-gradient problems numerically. We show that the optimized structure obtained offers significant gains in terms of ECF (by a factor of between 2 and 20) compared with non-optimized structures of the same volume, over a wide range of excitation frequencies. The procedure could open up new possibilities in the design of energy recovery systems without the use of piezoelectric materials.