The righteousness of God is Christ, who died on the cross for fulfilling God's righteousness. The kingdom of God is the evangelism to testify that Jesus is the Christ. 1 Cor 1:30, Rom 3:21, Rom 1:17, Rom 3:25-26, 2 Cor 5:21, Acts 1:3, Mt 28:18-19, Acts 1:8,
Jesus accomplished God's righteousness toward us by dying on the cross. (1 Cor 1:30, Rom 3:21, Rom 1:17, Rom 3:25-26, 2 Cor 5:21)
1 Cor 1:30 But of him are ye in Christ Jesus, who of God is made unto us wisdom, and righteousness, and sanctification, and redemption:
Rom 3:21 But now the righteousness of God without the law is manifested, being witnessed by the law and the prophets;
Rom 1:17 For therein is the righteousness of God revealed from faith to faith: as it is written, The just shall live by faith.
Rom 3:25 Whom God hath set forth to be a propitiation through faith in his blood, to declare his righteousness for the remission of sins that are past, through the forbearance of God; 26 To declare, I say, at this time his righteousness: that he might be just, and the justifier of him which believeth in Jesus.
2 Cor 5:21 For he hath made him to be sin for us, who knew no sin; that we might be made the righteousness of God in him.
Jesus commanded us to preach the gospel in order to establish the kingdom of God. (Acts 1:3, Mt 28:18-19, Acts 1:8)
Acts 1:3 To whom also he shewed himself alive after his passion by many infallible proofs, being seen of them forty days, and speaking of the things pertaining to the kingdom of God:
Mt 28:18 And Jesus came and spake unto them, saying, All power is given unto me in heaven and in earth. 19 Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost:
Acts 1:8 But ye shall receive power, after that the Holy Ghost is come upon you: and ye shall be witnesses unto me both in Jerusalem, and in all Judaea, and in Samaria, and unto the uttermost part of the earth.