The destruction is mutually assured. I hope Kim Jong Un knows that.
No it is not. North Korea can't destroy USA and her allies completely.
At best they might:
a) Fire off a nuke into South Korea (and conventional artillery and missiles as well) causing horrible damage to that country.
b) Perhaps fire a nuke into Japan.
c) If they improve their equipment fire one or two nukes into USA.
None of these would allow them to destroy their three main enemies, USA, Japan and South korea.
They can cause heavy casualties, mostly to civilians, and the nukes would certainly irradiate whatever they bomb but they do not have the firepower to destroy USA or Japan.
If the war is fought with conventional weapons only they could cause heavy casualties before collapsing but they would lose eventually because this time they would not get any help from Russia or China.
And if they fire the first nuke their country will be obliterated. The only objection china would have would be the fear of fallout spreading to their country. In fact China might even help curbstomp NK if it prevents others from using nukes.