Quantum anomalies give rise to new non-dissipative transport phenomena in relativistic fluids induced by external electromagnetic fields and vortices. These phenomena can be studied in holographic models with Chern-Simons couplings dual to anomalies in field theory. We perform a computation in AdS/CFT of the anomalous transport coefficients in a holographic massive gravity model, and find that the anomalous conductivities turn out to be independent of the holographic disorder couplings of the model. To arrive at this result we suggest a new definition of the energy-momentum tensor in presence of the gauge-gravitational Chern-Simons coupling. We also compute the electric DC conductivity and find that it vanishes for certain values of the disorder couplings.