WLC 191 is helpful here: "What do we pray for in the second petition? A. In the second petition (which is, Thy kingdom come,(1)) acknowledging ourselves and all mankind to be by nature under the dominion of sin and Satan,(2) we pray, that the kingdom of sin and Satan may be destroyed,(3) the gospel propagated throughout the world,(4) the Jews called,(5) the fulness of the Gentiles brought in;(6) the church furnished with all gospel-officers and ordinances,(7) purged from corruption,(8) countenanced and maintained by the civil magistrate
9) that the ordinances of Christ may be purely dispensed, and made effectual to the converting of those that are yet in their sins, and the confirming, comforting, and building up of those that are already converted
10) that Christ would rule in our hearts here,(11) and hasten the time of his second coming, and our reigning with him for ever
12) and that he would be pleased so to exercise the kingdom of his power in all the world, as may best conduce to these ends.(13)"
It is helpful to remember that our struggle under the New Covenant is no longer with flesh and blood as Paul says in Eph. 5. When we pray for the coming of the Kingdom, it is, in essence, a New Covenant imprecation. We ar asking God to destroy the kingdom of Satan and advance the gospel.