The gospels of Luke, Matthew and Mark are the synoptic gospels, that is, they can be seen together. The Gospel of John has a different style, it is the gospel of the spiritual rebirth and the eternal life.
In the Gospel of John there are 7 affirmations of the "I am" that are not found in the other Gospels. There is in the Book of Revelation an affirmation of "I am", totaling 8 affirmations like the 8 beatitudes in the Gospel of Saint Matthew. Remember that Thomas Aquinas express that each beatitude corresponds to a spiritual gift, the Beatitudes respond to the wisdom.
There is a relationship between the expression "Son of man" and the  "I am", in the Gospel of John, Jesus says:

When you have lifted up the Son of Man
then you will know that I Am. John 8:28

The concept of Son of man is found in the Book of Daniel, but in the Gospels it has a different meaning and the Apostle John is the one who best explains it. The affirmation Son of man synthesizes the 8 "I Am". Jesus in the Gospels uses the "I am" to affirm his divine origin.
The kingdom of God has two meanings: it is the man who seeks the spiritual gifts of God, that is, the man who becomes the son of God; and on the other side it is God who becomes son of man, that is, the spiritual gifts of God are personified in Christ.
To say that Jesus is the son of man is to say that he personifies the spiritual gifts, the perfections of God. Jesus affirming the "I am" is expressing that he is the "wisdom": I am the door, John 10: 9; I am the Bread of Life, John 6:34; that he is the "Eternal Life": I am the light, John 12:46. Spiritual gifts are perfections, not virtues.
Kingdom of God means dominion, empire of the divine gifts or perfections: dominion of wisdom, dominion of the constancy, dominion of the continuous improvement.
The idea or concept of the kingdom of God is partly philosophical (son of God) and partly theological (son of man).
The Kingdom of God can have a complementary meaning: "inside or outside of you", inside means the commandment of excellence: to live the spiritual gifts received from God; and outside: the government of those who emulate God through the gift of counsel.
The Kingdom of God is finally the fullness of the good among men.