The relationship between slaves and masters (and similarly, between employees and employers) should be guided by their commitment to the Lord and their desire to support each other in Christ. Christian slaves should obey their masters, and Christian masters should treat their slaves kindly (see Colossians 3:22–4:1).
Paul was not promoting slavery. Paul was teaching Christians how to live with it as a reality in that culture (for Paul’s views on slavery, see Philemon Book Introduction, "Meaning and Message").