The kingdom of God on earth is The Church of Jesus Christ of Latter-day Saints (D&C 65). The purpose of the Church is to prepare its members to live forever in the celestial kingdom or kingdom of heaven. However, the scriptures sometimes call the Church the kingdom of heaven, meaning that the Church is the kingdom of heaven on earth.
The Church of Jesus Christ of Latter-day Saints is the kingdom of God on the earth, but it is at present limited to an ecclesiastical kingdom. During the Millennium, the kingdom of God will be both political and ecclesiastical.