Sr4Fe6-xCoxO13+delta samples have been synthesized by a sol-gel procedure for 0 less than or equal to x less than or equal to 3 and the influence of firing temperature and procedure on the phase relationships has been investigated systematically. For a synthesis temperature of 1000 degrees C, X-ray diffraction data reveal that the samples with x less than or equal to 1.8 are single phase consisting of the intergrowth phase Sr4Fe6-xCoxO13+delta, while those with x>1.8 are composed of three phases - Sr4Fe6-xCoxO13+delta intergrowth phase, SrFe1-xCoxO3-delta perovskite phase, and Co3-xFexO4 spinel phase. Rietveld analysis of the X-ray diffraction data and thermogravimetric analysis of the samples reveal that the fraction of the perovskite phase increases as the synthesis temperature increases from 1000 to 1150 degrees C for x>1.8. For a given synthesis/annealing temperature, the sol-gel procedure favors a higher fraction of and higher solubility of Co in the intergrowth phase compared to the conventional solid state synthesis. In the single phase samples of the intergrowth oxide Sr4Fe6-xCoxO13+delta, the oxygen permeation flux at 900 degrees C decreases with increasing cobalt content x. On the other hand, the oxygen Aux increases with increasing x in the three phase samples due to an increasing amount of the SrFe1-xCoxO3-delta perovskite phase.