In order to map a flight for you on Singapore Air to Incheon, S. Korea I need the location you would be departing from to know what route you would need to take to get there.
The route that Singapore Air flies from Hong Kong to Incheon, South Korea varies depending on factors such as weather and daily flight patterns. Generally, it takes an open water approach flying parallel with China. Other flight patterns will take an inland flight approach with a landing to the West in South Korea.
by air it is about 8 to 7 hours
A trans-siberian air route is a no-stop travel between Europe and Japan or/and Korea.
The course that Singapore Air flys to South Korea varies depending on air traffic and weather patterns. The flight pattern typically flies over the Philippine Sea however it can take a more mainland approach if necessary.
14hr 10min Chicago OHare (ORD) to Seoul Incheon (ICN) by a nonstop flight operated by Korean Air.
14hr 40min Washington Dulles (IAD) to Seoul Incheon (ICN) by a nonstop flight operated by Korean Air.
12hr 50min to 12hr 55min San Francisco (SFO) to Seoul Incheon (ICN) by a nonstop flight operated by Singapore Airlines or Korean Air.
10hr 00min to 10hr 10min Seoul Incheon (ICN) to Sydney (SYD) by a nonstop flight operated by Qantas Airways, Korean Air or Asiana Airlines.
The air distance from Blenheim, New Zealand, to Incheon, New Zealand, is 6,204 miles. That equals 9,984 kilometers or 5,391 nautical miles.
06hr 10min to 06hr 25 min ICN to SIN by a nonstop flight operated by Asiana Airlines, Korean Air, Singapore Airlines, or US Airways.
If there were a direct flight, . . . about 12 or 13 hours depending on time of year, as seasonal jet streams can affect flight times. Still, there is no direct commercial flight. At best you would have to route yourself through Incheon, Korea's main international airport. Once you arrive in Incheon, you will need a 2 hour bus ride to Osan, which is just south of Seoul. With a destination such as Osan, I suspect you may be in the military. Osan Air Force Base may have military flights strictly for military personnel, but even those are probably routed through Japan. Good Luck!
Currently, the world's busiest air route was from Seoul-Gimpo to Jeju, in South Korea. Over 10 million passengers used that route in 2012.