There are two airlines that fly between Beijing PEK and Pyongyang FNJ: Koryo Airlines and Air China. While Koryo Airlines is cheaper than Air China, it isn’t the safest airline in the world. A r/t ticket with them costs approximately $700, while Air China is a bit more expensive (but safer).
Traditionally, Air China never released award inventory between PEK-FNJ. As of right now, there’s plenty of availability using the Aeroplan search engine. Interestingly, the United engine does not.
It is 20,000 AP points and $33 in fees for a round-trip ticket.
Note that for immigration requirements, you must be on a government approved tour. Consider both the security and immigration concerns before booking. However, lots of tourists, both Canadian and American, have gone to North Korea without incident, and have had an amazing time.
Thanks to UA Fan on Flyertalk for pointing this out!