The ground state of frustrated (antiferromagnetic) triangular molecular magnets is characterized by two total-spin S = 1/2 doublets with opposite chirality. According to a group theory analysis [M. Trif et al., Phys. Rev. Lett. 101, 217201 (2008)] an external electric field can efficiently couple these two chiral spin states, even when the spin-orbit interaction (SOI) is absent. The strength of this coupling, d, is determined by an off-diagonal matrix element of the dipole operator, which can be calculated by ab-initio methods [M. F. Islam et al., Phys. Rev. B 82, 155446 (2010)]. In this work we propose that Coulomb-blockade transport experiments in the cotunneling regime can provide a direct way to determine the spin-electric coupling strength. Indeed, an electric field generates a d-dependent splitting of the ground state manifold, which can be detected in the inelastic cotunneling conductance. Our theoretical analysis is supported by master-equation calculations of quantum transport in the cotunneling regime. We employ a Hubbard-model approach to elucidate the relationship between the Hubbard parameters t and U, and the spin-electric coupling constant d. This allows us to predict the regime in which the coupling constant d can be extracted from experiment.