We report experimental results of twin-domain size and bulk oxygen in-diffusion kinetics of YBa2Cu3O6+x, which supplement a previous and simultaneous study of the structural phase diagram and oxygen equilibrium partial pressure. Analysis of neutron powder diffraction peak broadening show features which are identified to result from temperature independent twin-domain formation in to different orthorhombic phases with domain sizes 250 and 350 angstrom, respectively. The oxygen in-diffusion flow shows simple relaxation type behaviour J = J0 exp(-t/tau) despite a rather broad particle size distribution. At higher temperatures, tau is activated with activation energies 0.55 and 0.25 eV in the tetragonal and orthorhombic phases, respectively. Comparison between twin-domain sizes and bulk oxygen in-diffusion time constants indicates that the twin-domain boundaries may contribute to the effective bulk oxygen in-diffusion. All our results may be interpreted in terms of the 2D ASYNNNI model description of the oxygen basal plane ordering, and they suggest that recent first principles interaction parameters should be modified.