Is the Taplejung / Sukhetar airport open? YES! Sukhetar (the airstrip 8km above Taplejung) opened in October 2015. Sadly many flights were cancelled shortly after due to the lack of aviation fuel caused by the border blockades, however this seems to be resolved now
As of March 2016 flights are running normally
Tara air (Yeti subsidiary) run flights on Fridays
Goma have flights on Mondays and Fridays
Nepal Airlines have flights on Wednesdays, Thursdays and Sundays
Nepal Airlines are a subsidised airline and therefore slightly cheaper than the others. However they book up well in advance.
Check with Flight Connections or directly with the airlines for updates
Reaching Taplejung by air is by far the easiest way to start the Kanchenjunga Trek.
Here is the airport as it used to be. Looks good for cricket outside of landing hours.