Does Paul ever teach that repentance and baptism are required for salvation?
No. Paul does not teach that repentance and baptism are required for salvation. His gospel is that Christ died for our sins, was buried, and rose again, and that one must believe on the Lord Jesus Christ. Repentance and baptism belonged to Israel's program, not Paul's gospel.
Les explains that Paul's gospel is distinct: when the jailer asked what he must do, Paul answered, "Believe on the Lord Jesus Christ." Paul's one gospel is that Christ died for our sins, was buried, and rose again. Les challenges listeners to search Paul's letters from Romans through Hebrews for any place where Paul teaches repentance and baptism for salvation, and says you will not find it because Paul does not teach it or preach it. Repentance and baptism belonged to Israel's program, as when Peter said, "Repent and be baptized." But to the Gentile the requirement is simply to believe the gospel. These are different economies, and they cannot be mixed.