China will let Kim continue to issue threats but at the first sign that he is actually going to carry out a threat, they will get rid of Kim for us. Why? Because China owns a lot of American debt and anything that would reduce the value of the dollar (like a war) means American payments on their debt will be made with money that has little value. Even where payments are specified in gold, they don't want America to have trouble coming up with the payment or the lifestyle of the Communist elite may suffer. When Kim Jong Un took over from Kim Jong Il a few years ago, there was the same sabre rattling. South Korea took little notice and my daughter was there in Pohang as an English teacher and no one seemed concerned.
America would not use nuclear weapons against North Korea. China and South Korea would be at risk. But the US has a fantastic array of conventional weapons that could total all of their missile launch facilities.