The odds are that he will fly his Russian made Il-62M aircraft to Singapore despite his plane having never flown that far before:
How will North Korean leader Kim Jong-un travel the 4,700km to Singapore, where the North Korea-US summit will be taking place on June 12? Since a train journey from North Korea to Singapore is out of the question, attention is focusing on Kim’s official airplane, Chammae-1 (meaning goshawk, North Korea’s national bird).On May 7, Kim flew Chammae-1 to Dalian in China’s Liaoning Province to hold his second summit with Chinese President Xi Jinping.
Pyongyang and Dalian are about 360km apart in a direct line. Chammae-1, a souped-up IL-62M of Soviet manufacture, is equipped with four engines, which gives it a maximum flight distance of 9,000-10,000km. These specifications make it fully capable of reaching Singapore, which is about 4,700km away from Pyongyang.But safety concerns have also been raised since Kim’s jet is old and has never attempted a long flight before. The IL-62M, an upgraded version of the IL-62 model that was developed in 1967, entered production in 1975 and was discontinued in 1995.“[Chammae-1] is presumed to have been manufactured in 1985, and provided that it’s in good repair, it will have no problem flying to Singapore. But since it has no experience with long-distance flight and may not have been serviced properly, it probably presents a dilemma [for North Korea],” said a source in the South Korean government.
In Nov. 2014, Choe Ryong-hae, vice chairman of the Korean Workers’ Party (KWP), was reportedly on a flight to Russia as a special envoy for Kim Jong-un when a problem with his aircraft forced him to return to Pyongyang and restart his journey. The aircraft that Choe and his party were on was apparently also an IL-62. This is leading to speculation that Kim may have a stopover in China or borrow a large charter plane from China. [Hankyoreh]
You can read more at the link, but I seriously doubt Kim Jong-un would take a charter plane from China to Singapore. It would be too embarrassing in my opinion for him to show up in Singapore not flying in a state sponsored aircraft.