At the end of Dragon Ball, when the Ox King was trapped, Goku flew into the fire on the Nimbus and had an extended conversation with the Ox King. Goku's previous demonstrations of strength also implied that he would have no problem lifting and holding on to the Ox King.
I did not read the manga, I only watched the anime. Is any specific reason given or implied why Goku could not have grabbed the Ox King at that time and carried him (either on the cloud or hanging onto him if Ox King could not fit or ride) out of the flames to buy himself and Chi Chi extra time to find a way to extinguish the flames?