Hey, John.
You’ve already received some good answers in relation to how “the kingdom of God” and “the kingdom of heaven” are synonymous and in relation to what they are, so I’ll just focus upon “the kingdom IN heaven” in my response.
Turning to the very first verse of the Bible, we read:
“In the beginning God created the heaven and the earth.” (Genesis 1:1)
Although the underlying Hebrew word “šāmayim” is translated here in the singular as “heaven” in the KJV, the suffix “-im” in Hebrew is plural, and it is the equivalent of our “s” in the English language:
https://www.blueletterbible.org/lexicon/h8064/kjv/wlc/0-1/
With such being the case, this verse would be better translated to read:
“In the beginning God created the heavens and the earth.” (Genesis 1:1)
In fact, this same underlying Hebrew word is translated in the plural as “heavens” as early as Genesis chapter 2, where we read:
“Thus the heavens and the earth were finished, and all the host of them.” (Genesis 2:1)
As I trust you already know, the Bible speaks of three distinct “heavens”, with “the third heaven” being the place where both God the Father and Jesus presently dwell.
In relation to the same, we read:
II Corinthians chapter 12
[1] It is not expedient for me doubtless to glory. I will come to visions and revelations of the Lord.
[2] I knew a man in Christ above fourteen years ago, (whether in the body, I cannot tell; or whether out of the body, I cannot tell: God knoweth) such an one CAUGHT UP TO THE THIRD HEAVEN.
[3] And I knew such a man, (whether in the body, or out of the body, I cannot tell: God knoweth)
[4] How that he was CAUGHT UP INTO PARADISE, and heard unspeakable words, which it is not lawful for a man to utter.
The Apostle Paul was “caught up to the third heaven” or “caught up into paradise” where he received “revelations of the Lord” and “heard unspeakable words, which it is not lawful for man to utter”.
In other words, this is the place where God and Jesus presently dwell.
Although the creation account in Genesis chapter 1 doesn’t really tell us anything about “the third heaven”, we are told much about it elsewhere in scripture.
For example, we know that there is a Jerusalem in “the third heaven” from portions of scripture such as these:
“But JERUSALEM WHICH IS ABOVE is free, which is the mother of us all.” (Galatians 4:26)
Again:
“But ye are come unto mount Sion, and unto the city of the living God, THE HEAVENLY JERUSALEM, and to an innumerable company of angels,” (Hebrews 12:22)
Furthermore, we know that there is a temple in “the third heaven” or in “the heavenly Jerusalem”.
In relation to the same, we read:
Hebrews chapter 8
[1] Now of the things which we have spoken this is the sum: We have such an high priest, who is set on the right hand of the throne of the Majesty in the heavens;
[2] A minister of the sanctuary, and of THE TRUE TABERNACLE, WHICH THE LORD PITCHED, AND NOT MAN.
[3] For every high priest is ordained to offer gifts and sacrifices: wherefore it is of necessity that this man have somewhat also to offer.
[4] For if he were on earth, he should not be a priest, seeing that there are priests that offer gifts according to the law:
[5] WHO SERVE UNTO THE EXAMPLE AND SHADOW OF HEAVENLY THINGS, AS MOSES WAS ADMONISHED OF GOD WHEN HE WAS ABOUT TO MAKE THE TABERNACLE: FOR, SEE, SAITH HE, THAT THOU MAKE ALL THINGS ACCORDING TO THE PATTERN SHEWED TO THEE IN THE MOUNT.
The earthy tabernacle which Moses pitched merely “served unto the example and shadow of heavenly things” in that it was an earthly representation of “the true tabernacle, which the Lord pitched, and not man” or the true tabernacle in “the third heaven”. This is “the pattern” that Moses was “shown in the mount”.
In relation to the same, we read:
Exodus chapter 25
[8] And let them make me a sanctuary; that I may dwell among them.
[9] According to all that I shew thee, after the pattern of the tabernacle, and the pattern of all the instruments thereof, even so shall ye make it.
Moses was not only given “the pattern of the tabernacle” that the Lord pitched in “the third heaven”, but he was also given “the pattern of all the instruments thereof”.
For example, we read several times in the Old Testament or in the Old Covenant about “the ark of the testimony” (Exod. 25:22, 26:33, etc.) or “the ark of the covenant” (Num. 10:33, 14:44, etc.) in relation to a tabernacle or temple here on earth, and we similarly read in the New Testament or in the New Covenant about “the ark of the testament” in the temple of God in heaven:
“And THE TEMPLE OF GOD WAS OPENED IN HEAVEN, AND THERE WAS SEEN IN HIS TEMPLE THE ARK OF HIS TESTAMENT: and there were lightnings, and voices, and thunderings, and an earthquake, and great hail.” (Revelation 11:19)
Further still, there’s not only a heavenly Jerusalem, and a heavenly temple full of heavenly instruments, but Isaiah actually saw the pre-incarnate Christ sitting upon a throne in heaven as “the King”.
In relation to the same, we read:
Isaiah chapter 6
[1] In the year that king Uzziah died I SAW ALSO THE LORD SITTING UPON A THRONE, high and lifted up, AND HIS TRAIN FILLED THE TEMPLE.
[2] Above it stood the seraphims: each one had six wings; with twain he covered his face, and with twain he covered his feet, and with twain he did fly.
[3] And one cried unto another, and said, Holy, holy, holy, is the LORD of hosts: the whole earth is full of his glory.
[4] And the posts of the door moved at the voice of him that cried, and the house was filled with smoke.
[5] Then said I, Woe is me! for I am undone; because I am a man of unclean lips, and I dwell in the midst of a people of unclean lips: FOR MINE EYES HAVE SEEN THE KING, the LORD of hosts.
[6] Then flew one of the seraphims unto me, having a live coal in his hand, which he had taken with the tongs from off the altar:
[7] And he laid it upon my mouth, and said, Lo, this hath touched thy lips; and thine iniquity is taken away, and thy sin purged.
[8] Also I heard the voice of the Lord, saying, Whom shall I send, and who will go for us? Then said I, Here am I; send me.
[9] And he said, Go, and tell this people, Hear ye indeed, but understand not; and see ye indeed, but perceive not.
[10] Make the heart of this people fat, and make their ears heavy, and shut their eyes; lest they see with their eyes, and hear with their ears, and understand with their heart, and convert, and be healed.
We can know, of a certainty, that this King whom Isaiah saw sitting upon a throne in the temple in heaven was, in fact, Jesus:
John chapter 12
[39] Therefore they could not believe, because that Esaias said again,
[40] He hath blinded their eyes, and hardened their heart; that they should not see with their eyes, nor understand with their heart, and be converted, and I should heal them.
[41] THESE THINGS SAID ESAIAS, WHEN HE SAW HIS GLORY, AND SPAKE OF HIM.
Based upon portions of scripture like these, and this is by no means an exhaustive list, we can safely conclude the following:
1. There is a heavenly Jerusalem.
2. There is a temple in the heavenly Jerusalem.
3. Jesus Christ sits upon a throne inside the temple in the heavenly Jerusalem, and he is the King.
If we come to properly understand this, then we can also properly understand why God called the nation of Israel to initially represent him on this earth.
In other words, Israel’s kings, reigning from within a temple in Jerusalem, were supposed to represent the true King, Jesus Christ, and his temple in the heavenly Jerusalem to all the inhabitants of this earth.
Sad to say, more often than not, they terribly failed to do so, and their worst is yet to come.
Yes, they will ultimately broker a deal with the literal antichrist who will briefly reign within a rebuilt temple in Jerusalem prior to the second coming of Christ.
Anyhow, I said all of that to say this:
Jesus taught his disciples to pray, “Thy kingdom come”, and it ultimately will come.
Yes, “the kingdom IN heaven” will one day be truly represented right here on earth at Christ’s second coming.
I hope that this helps.