We report on the mechanism and energy barrier for oxygen diffusion in tetragonal La(2)CoO(4+δ). The first principles-based calculations in the Density Functional Theory (DFT) formalism were performed to precisely describe the dominant migration paths for the interstitial oxygen atom in La(2)CoO(4+δ). Atomistic simulations using molecular dynamics (MD) were performed to quantify the temperature dependent collective diffusivity, and to enable a comparison of the diffusion barriers found from the force field-based simulations to those obtained from the first principles-based calculations. Both techniques consistently predict that oxygen migrates dominantly via an interstitialcy mechanism. The single interstitialcy migration path involves the removal of an apical lattice oxygen atom out from the LaO-plane and placing it into the nearest available interstitial site, whilst the original interstitial replaces the displaced apical oxygen on the LaO-plane. The facile migration of the interstitial oxygen in this path is enabled by the cooperative titling-untilting of the CoO(6) octahedron. DFT calculations indicate that this process has an activation energy significantly lower than that of the direct interstitial site exchange mechanism. For 800-1000 K, the MD diffusivities are consistent with the available experimental data within one order of magnitude. The DFT- and the MD-predictions suggest that the diffusion barrier for the interstitialcy mechanism is within 0.31-0.80 eV. The identified migration path, activation energies and diffusivities, and the associated uncertainties are discussed in the context of the previous experimental and theoretical results from the related Ruddlesden-Popper structures.