I am no friend of Trump, as some of you know - #NeverTrump - but even so, it really irks me when people say Trump shouldn't be president because he might start a nuclear war.
The plain, blunt fact of the matter is, the president cannot unilaterally order a nuclear strike. The president's role is initiating the sequence - nobody can launch a nuke unless the president initiated the order - but the final go-order is not sent to the missile silos until the Secretary of Defense has countersigned the order. The president can, of course, fire the individual secretary who refuses to countersign his order, but he still has to get the order countersigned, and so he must then move on to the individual who succeeds to the fired secretary. However, the president cannot simply go through a "massacre" of acting secretaries unfettered; the vice president and a majority of the heads of the executive departments can remove the president (25th Amendment).
In other words, yes, a president could launch a nuclear strike if he managed to carefully pick a secretary of defense who would rubber-stamp his orders, and managed to carefully pick a vice president (and/or a majority of the executive heads) who would rubber-stamp his orders, but short of that, no, a president cannot unilaterally order a nuclear strike without out adequate provocation from the target of the strike.
In other words, Donald Trump, if he were to become president, could not start a nuclear war by launching a nuclear strike except under circumstances in which any other president would almost certainly launch a strike as well, or at least, would be well-justified in launching such a strike.