We consider general black hole solutions of Einstein-Maxwell-scalar theory
that are holographically dual to conformal field theories at finite charge
density with non-vanishing magnetic fields and local magnetisation currents,
which generically break translation invariance explicitly. We show that the
thermoelectric DC conductivity of the field theory can be obtained by solving a
system of generalised Stokes equations on the black hole horizon. For various
examples, including Q-lattices and one-dimensional lattices, we solve the
Stokes equations explicitly and obtain expressions for the DC conductivity in
terms of the solution at the black hole horizon.