The term “kingdom of God” is another way that Luke presents Paul’s case for Jesus as the Messiah who fulfills promise (18:5, 19). Marshall (1980: 309) says that Paul preaches Jesus and the kingdom. For Paul, the two are bound up together in the gospel.
The expression appears in the OT regarding Pharaoh (Exod. 8:15; 9:35) and of the people in the wilderness (Deut. 2:30). It is rarely used in the NT but always with this same force (Heb. 3:8, 13, 15; 4:7; Rom. 9:18).