Many of us are familiar with or know by rote the Lord's Prayer (and if you're not, you can see how Christ said it here). All to say, I remember talking with a friend of Christ's kingdom coming when I was in high school, and I am super glad that it never happened as we discussed. Essentially, our vision of Him coming was on a blazing chariot with weapons unimaginable, flying from the heavens and mowing down the infidels. My belief of the coming of the kingdom was too much like the Jews' belief system when Christ first came - that a warrior king would come to decimate all who were not part of his chosen people. When he comes again, I suppose that will be the matter, but when he comes now he comes to kill the old man in us and to make us new.
I'm thankful for that because case in fact, he would have been mowing down me had his kingdom come in such a militant way.
When Jesus preached of the kingdom, he talked about it as being the possession of children, those who are poor, and those who are poor in spirit. He preached that the coming of the kingdom came in hand with the preaching of His gospel.
So, if this is an issue that we care about (namely, the coming of the kingdom) and North Korea is something we worry about (as, I assume, some do), then I would say that our responsibility to this is to pray for the country and give to the effort of evangelism and missions there. I don't think that this is responsibility for everyone, because everyone doesn't care about what happens there (not to be curt, it's just the reality of the situation) and God hasn't necessarily called any of us to give all of ourselves to all causes for the Kingdom (just that we would give all of our self to the cause of the kingdom - period).
How does this play out? Brian Prentiss introduced me to Luther's commentary on the Lord's Prayer a few years ago and I think that it would bless your prayer life richly regarding subjects such as this. Essentially, to pray "Thy Kingdom Come" is to pray that his Kingdom would come by faith and also by power. We are praying that the word of his power would work to turn hearts and to make his kingdom a reality in this present life while we are also praying that the power of Christ would come to destroy the kingdom of the ruler of this world once and for all that we might be separated from this body of sin.
What's so interesting is that I think that we most often don't believe in His power to make this happen in the reality of this present life. During a recent "Mission's Conference," I went to two talks given by people who were laboring in closed countries. One of them had labored in China and is now doing so in N. Korea. The vehicle he uses is education, and the N. Korean government is aware of this. They had an official stay at his school in China, the official witnessed the professor sharing the gospel of Jesus to students, and Kim Jong Il himself requested that this school be brought to N. Korea.
To the missionaries in either of these countries, the same question was asked (in fact, it was the first question asked in both talks and I think that people in the audience even interrupted them to ask this) "How can you do your work under such an oppressive government," or something along those lines. Neither of them skipped a beat in answering that it was the power of God and the immutable working of His providence that allowed them to do what they do.
We see some man like Kim Jong Il and believe that the only way we can fight him is with the weapons of this world. In fact, God is much more powerful than this. The Word is much more powerful than this. Still, we continue to wish and subject the people under him to shameful sanctions in belief that He himself is suffering without understanding that he is seen as a god in his country and he rules with fear. We can allow our government to deal as it will with the country, but our response (if the Lord has laid that specific country on our hearts) is not to wish ill upon our enemies, but to love our enemies.
I'll be honest, that's hard for me to swallow.
However, if I believe the gospel, then I believe that's how God has loved me. Can we dare to believe that God does in fact work supernaturally? Can we dare to trust that God can work in the hardened hearts of men? If we can't, are we to even begin to believe the gospel?