Did Jesus, in fact, approve of slavery? I do not think so, but He was not about to launch a crusade against it because to do so would have been an exercise in futility.
Slavery was a timeless tradition among His own people as well as an integral element of Roman society.
What Jesus and the Apostles did, however, was to preach and live the Good News; proclaiming that, in God's sight, all humankind is equal. To the world of Jesus, Peter and Paul, this was a radical teaching and for those who believed, especially slaves, a wondrous revelation.
This was a time when Rome dominated the known world and when fully one third of the population of Rome was made up of slaves. With some exceptions, slaves in the Roman Empire, including Palestine, were better off than most of the street people of our modern cities. You see THEY were valuable property, THEY were commercially significant.
Roman law protected slaves from serious abuse, guaranteed them many basic human rights, including a place to live, and Christian morality insisted upon their dignity as subjects of Divine love and redemption. Slaves who were not born into slavery were prisoners of war and of the courts, abandoned children and, occasionally, victims of kidnapping. A high proportion of slaves eventually won their freedom and some of them rose to high positions in society.
Jesus reflected the mindset of His day when in rebuking His listeners for being overly proud of their spiritual accomplishments, He compared their concept of God being somehow indebted to them, to the patently ridiculous scenario of a master being indebted to his slave simply because the slave honoured the master's will.
No, Jesus did not fight slavery. A slave had his or her place. It was not an easy life at its best and it was a horrible, demeaning and demanding life at its worst, but, on the whole, it was better than dying of exposure, from hunger or by the sword. And Jesus and the Church that followed Him were very much aware of that.
One cannot but observe that the slave driven economy of the18th and 19th century Americas, and the slightly modified versions we continue to support in the 3rd world, is a much crueler reality than that which was accepted by Jesus and His followers.
This is a slavery that Jesus would have US confront in the name of justice and to do so without any thought of reward other than knowing that we are doing His will. You know what that means? ...That's right! Choosing to be a slave of Jesus Christ!