The gospel of the kingdom is the good news given to the Jews of their promised kingdom, a literal, physical kingdom on earth where Christ is King. The gospel of the grace of God is the good news preached by Paul given by the Holy Spirit explaining the death, burial, and resurrection or Jesus Christ for the forgiveness of sins.
Matthew 9:35, "And Jesus went about all the cities and villages, teaching in their synagogues, and preaching the gospel of the kingdom, and healing every sickness and every disease among the people."
1 Corinthians 15:1-4, "Moreover, brethren, I declare unto you the gospel which I preached unto you, which also ye have received, and wherein ye stand; By which also ye are saved,...how that Christ died for our sins according to the scriptures; And that he was buried, and that he rose again on the third day according to the scriptures;"
Concerning the gospel of the Kingdom of God, I belonged to a cult, the Armstrongites, which made the "gospel of the kingdom of God" into an exclusive reference to the eschatological reign of Jesus Christ in the Millennium. They de-emphasized the personal salvation part of the gospel, and made it all about the Millennial reign of Christ. Additionally, they taught that other Christians were ignorant about the Millennial reign of Christ, which was a total misrepresentation because almost all evangelical Christians I know understand the Millennial reign. Some may disagree with particular aspects of when it begins, such as amillenial or postmillennial people, but they understand the concept.
The concept of the "kingdom of God" is much more comprehensive than the Armstrongites taught. It refers to the sphere of God's influence. The sphere of God's influence on earth was increased when Christ dwelt amongst us in flesh. It is increasing exponentially with the conversion of each new person, as they are added to the Church. It will increase exponentially when Christ appears again, and the Millennium is established and thereafter.
So, I don't view the kingdom of God and the gospel of salvation to be contradictory. It has to do with the sphere of God's influence. This is also consistent with the idea of the government of God over the individual, the church, and the entire world someday.
Note that I am not denying that God is fully sovereign now, but that his sphere of influence is more obvious as those who are converted are being added to the Church and coming under God's rulership in their lives.
Here's a few verses related to this:
Matthew 13:
31He put another parable before them, saying, “The kingdom of heaven is like a grain of mustard seed that a man took and sowed in his field.
32It is the smallest of all seeds, but when it has grown it is larger than all the garden plants and becomes a tree, so that the birds of the air come and make nests in its branches.”
33He told them another parable. “The kingdom of heaven is like leaven that a woman took and hid in three measures of flour, till it was all leavened.”