The Cold War had nothing to do with the Vietnamese Rebellion of the 1960's. In this timeline the Vietnamese are fed up with the French. The French didn't want Vietnam to be independent (Colonial Power etc.) so the Vietnamese rebelled by force.
The Vietnamese rebellion (1959-1965)
The Vietnamese used Guerrilla Warfare throughout their war for independence. The French would try to land forces on the ground just to have them mowed down from all different directions. It's estimated over 25,000 French troops died trying to storm the beaches of Vietnam. The Vietnamese won the war simply by patience and tactics. There were no significant battles as French troops never made it to any city or village.
Vietnam is not modern (by this I mean it's even less modern than OTL). The name Kingdom is very misleading as there is no authority with the Monarchy, the Monarchy is purely ceremonial (much like the Commonwealth).