I think the most reliable extant sources of what Jesus taught about the kingdom of God the gospel books called "According to Mark" and "According to Matthew". The message is that the kingdom of God is as follows. It is near, very near, even at hand (Mark 1:1, 4-5, 14-15; Matthew 3:1-2, 7-12) and that the kingdom is the god's rule on the Earth (at least over Judea) through the messianic son of man. The son of man would rule on Earth. In order to enter the kingdom and receive its blessings people would have to obey the god's laws and seek righteousness, including loving one's neighbor as oneself, and by striving hard to get into the kingdom (Matthew chapters 5 through 7; 18:7-9). Jesus' message about the kingdom was an apocalyptic one (Matthew 13:1-52; 16:27-28; chapters 24-25). The existing political systems and the existing economic systems would be overturned by the kingdom. Many of the poor and of the oppressed would become blessed (Matthew 9:35-38) and most of the rich would suffer and fail to enter the kingdom (Matthew 19:23-24). Those existing in slavery would be released from bondage. Those who worshiped the god properly would be cured of infirmities and of diseases and would receive long life (Matthew 4:23; 10:7-8; 11:2-6; 14:14; 15:30-39). The dead would raised to life (Matthew 10:8; 27:51-53). The resurrected righteous dead would be greatly rewarded and the resurrected unrighteous dead would be judged and receive contempt (John 5;28-29; Daniel 12:2; John 11:24).
Reading what H.G. Wells' said about Jesus in Wells' two volume book called The Outline Of History: Being A Palin History Of Life And Mankind (but note the subtitle on the cover of the book is "The Whole Story Of Man") contributed to be once again believing that Jesus was a historical person. [The edition I read is the final revised edition, revised by Raymond Postgate and G. P. Wells, bearing the copyright date of 1971.] That is because I saw how his apocalyptic message, including a number of hard sayings for those who were prosperous, indicate that Jesus of Galilee must have existed as the founder (or probably a co-founder along with John the baptist/baptizer) of the Nazarene movement within Judaism which later evolved (largely due to Saul/Paul of Tarsus) into what became known as Christianity.
The apocalyptic message of Jesus failed to come true (other than the
destruction of Jerusalem). The kingdom of the god did not become
established upon Earth throughout the Earth, nor even upon Judea.
Page 445 of Wells' book says the following.
"....remarkable is the enormous prominence given by Jesus to the teaching of what he called the Kingdom of Heaven, and its comparative insignificance in the procedure and teaching of most of the Christian churches.
This doctrine of the Kingdom Heaven, which was the main teachings of Jesus, and which plays so small a part in the Christian creeds, is certainly one of the most revolutionary doctrines that ever stirred and changed human thought.
... For the doctrine of the Kingdom of Heaven,a s Jesus seems to have preached it, was no less than a bold and uncompromising demand for a complete change and cleansing of the life of our struggling race, an utter cleansing without and within."
