Multiphase magnetoelectric (ME) composites deposited on flexible substrates have been widely studied, which can respond to ambient mechanical, magnetic, and electric field excitations. This paper reports an investigation of flexible FeCoSiB/ZnO thin-film generators for low-frequency energy harvesting based on three substrates. Both hard substrate Si and flexible substrates (Polyethylene terephthalate (PET) and Polyimide (PI)) are adopted to make a comparison of energy conversion efficiency. For the single ME laminate, a PET-based flexible ME generator presents the best ME coupling performance with an average coupling voltage output of ~0.643 mV and power output of ~41.3 nW under the alternating magnetic field of 40 Oe and 20 Hz. The corresponding ME coupling coefficient reaches the value of 321.5 mV/(cm·Oe) for this micrometer scale harvester. Flexible ME modules with double cantilevered ME generators are further designed and fabricated. When two PET-based generators are connected in series, the average voltage output and power are ~0.067 mV and ~0.447 nW, respectively. Although the energy harvested by ME thin-film generators is much smaller than bulk multiferroic materials, it proves the feasibility of using flexible FeCoSiB/ZnO generators for harvesting ambient magnetic energy and supplying sustainable electronic devices in the future.