Processes with precisely known cross sections, like neutrino-electron elastic scattering (νe-→νe-) and inverse muon decay (νμe-→μ-νe) have been used by MINERνA to constrain the uncertainty on the neutrinos at the main injector (NuMI) neutrino beam flux. This work presents a new measurement of neutrino elastic scattering with electrons using the medium energy ν¯μ-enhanced NuMI beam. A sample of 578 events after background subtraction is used in combination with the previous measurement on the νμ beam and the inverse muon decay measurement to reduce the uncertainty on the νμ flux in the νμ-enhanced beam from 7.6% to 3.3% and the ν¯μ flux in the ν¯μ-enhanced beam from 7.8% to 4.7%.