The Kingdom of God
And when he was demanded of the Pharisees, when the kingdom of God should come, he answered them and said, The kingdom of God cometh not with observation: Neither shall they say, Lo here! or, lo there! for, behold, the kingdom of God is within you.
- Luke 17:20-21 (KJV)
A lot of people have suggested that the Greek word "entos" should have been translated "in the midst of" instead of "within you". In that way, Jesus would be the Kingdom of God, and in the midst of them. However that can't be right, because if that were the case people would then still be able to say "Lo here! or, lo there!". So that can't be right.
If the Kingdom of God is "within you", it must mean that God somehow rules in our hearts.
For as many as are led by the Spirit of God, they are the sons of God.
- Romans 8:14 (KJV)
The Holy Spirit makes sure we keep God's Law, the Ten Commandments.
A new heart also will I give you, and a new spirit will I put within you: and I will take away the stony heart out of your flesh, and I will give you an heart of flesh. And I will put my spirit within you, and cause you to walk in my statutes, and ye shall keep my judgments, and do them.
- Ezekiel 36:26-27 (KJV)
Our bodies are also temples of the Holy Spirit.
What? know ye not that your body is the temple of the Holy Ghost which is in you, which ye have of God, and ye are not your own?
- 1 Corinthians 6:19 (KJV)
And here is how Ellen White puts it.
Not by the decisions of courts or councils or legislative assemblies, not by the patronage of worldly great men, is the kingdom of Christ established, but by the implanting of Christ's nature in humanity through the work of the Holy Spirit. "As many as received Him, to them gave He power to become the sons of God, even to them that believe on His name: which were born, not of blood, nor of the will of the flesh, nor of the will of man, but of God." John 1:12,13. Here is the only power that can work the uplifting of mankind. And the human agency for the accomplishment of this work is the teaching and practicing of the word of God.
- Ellen White, The Desire of Ages, p. 509/510
So yes, the phrase that the Kingdom of God is "within you" is correct.
The kingdom of God is a spiritual kingdom. It is the Holy Spirit that reigns in your heart.