To preach on the kingdom of God means to preach the word of the Lord Jesus, for we see Paul in the synagogue in Ephesus speaking on the things concerning the kingdom God,
And he went into the synagogue and spoke boldly for three months, reasoning and persuading concerning the things of the kingdom of God (Acts 19:8).
Later some of the Jews opposed Paul’s teaching, and he moved to a new location, this time a school in the city,
But when some were hardened and did not believe, but spoke evil of the Way before the multitude, he departed from them and withdrew the disciples, reasoning daily in the school of Tyrannus (Acts 19:9).
What resulted? Luke informs us that in a relatively short time, the word of Jesus spread throughout Asia,
And this continued for two years, so that all who dwelt in Asia heard the word of the Lord Jesus, both Jews and Greeks (Acts 19:10).
Jews and Greeks heard the things concerning the kingdom of God, which meant they heard the word of the Lord Jesus, because as Lord He has a kingdom, and if we want Him, we must be in His kingdom, which is the church.