The zeroth law of Thermodynamics is speaking about systems already at thermodynamic equilibrium. It does not say anything about the time required to get equilibrium. The equilibration time depends on the efficiency of the exchanges of energy (not only thermal exchanges but also volume variations and particle exchanges, in simple systems) and their relaxation times.
Macroscopic transport theories, like heat conduction or diffusion theory, may provide some generic guide, but they depend on non-thermodynamic quantities (the transport coefficients like thermal conduction coefficient, viscosity coefficients, diffusion, and inter-diffusion coefficients) whose determination requires some detailed model of the underlying atomic processes. Moreover, macroscopic solutions for the time relaxation towards equilibrium, often providing exponentially decaying behaviors, shouldn't be taken too seriously when the difference of thermodynamic state variables becomes comparable with the size of thermodynamic fluctuations always present in finite-size samples.
As a consequence, the time to reach thermodynamic equilibrium is strongly dependent on all the relaxation times in a system. In practice, what really matters is the presence of a well definite macroscopic time scale such that the system properties are stationary. I often like to cite Feynman's definition of thermodynamic equilibrium, given at the beginning of his Statistical Mechanics textbook: it is the state such that "all the "fast" things have happened and all the "slow" things not.