I'm mixed. I honestly don't think Trump can just say we're going to war, and we go to war. Even amongst republicans, there would be push back from guys like McCain. Plus, he campaigned that Hillary would get us into WW3, but he would keep us out of conflict. Given his slipping support, even amongst republicans, and his base. I just don't see people rallying behind him. Even more so as most polls show people don't trust him as president period, let alone if he leads us into a nuclear war.
That said, do I think it's possible Trump could tweet in protest if he watches a story saying he's weak on NK? Sure, entirely possible. Just like with the transgender tweet, generals did not immediately support it. Then later they scrambled to turn it into policy. I could see Trump tweeting something that gives the Pentagon a heart attack, and then his handlers, and generals have to talk it back.
The truth is, all of this is new. Trump has proven time, and time again that he's unique, and unpredictable as president. We really don't know what he'll tweet from his toilet at 5 am tomorrow. We also don't know if NK will take it serious, or not.
I think that's the problem. In a normal presidency, suggesting a president would randomly say he's starting war with NK with no build up would be laughable. The president usually brings his case to the people, congress, and the senate. Trump isn't a normal president. We really don't know what newscast may set him off, and straight to twitter.