In fact, Kim will react in exactly the opposite manner. He will redouble his country's efforts to perfect a missile which can strike North America, as well as completing the DPRK's miniaturization of nuclear weapons so they can ride along.
Syria is nothing like North Korea. Syria has no weapons which could strike the U.S. and has never threatened such a move against U.S. forces in the region. One of the Islamist groups which wants to replace Assad with a government run under sharia, Jaysh al-Islam (Army of Islam), praised the missile strike because it will make its job easier. 91% of Iraqis want to make sharia the law of the land and 38% want to make it apply to everyone, both Muslim and non-Muslim (for Iraq's next-door neighbor, Jordan, those figures are 71% and 58%). Hawaii Congresswoman Tulsi Gabbard, someone who Democrats should be grooming for vice president in 2020, expressed dismay at the missile strike because most of the Syrian government's opposition is Islamist, though the indiscriminate killing of children via chemical weapons is a redline even Barack Obama could understand.
The U.S. might be able to destroy all North Korean nuclear and missile facilities in a single attack, though the mobile missile launchers that were supplied by China may be problematic. The DPRK is developing ballistic missile submarines, but given how few of them exist, the U.S. Navy can tail them until the order is given to destroy them.
But the elephant in the room will always be the 10,000-20,000 artillery pieces situated just north of the DMZ, well within range of Seoul, with them being located in reinforced bunkers to prevent them from being destroyed by carpet bombing or artillery fire. Kim's father, Kim Jong-il, knew that this artillery, employing both traditional and chemical munitions, was an ace in the hole because we could not possibly destroy them all before they cause hundreds of thousands, if not millions of casualties in South Korea.
As I keep saying, the only solution is to coerce China into eliminating Kim and his henchmen. We could make a deal with China to remove all U.S. ground forces after a reunification of Korea under UN terms, not to mention that the THAAD missiles China hates so much would not be deployed. But the current situation is going to end badly.