For 21 years, the King has flown with KLM and before that for Martinair for twice a month. Often on short flights within Europe (KLM Cityhopper).
The King is re-training to be able to fly a Boeing 737 in the future, so he will be able to not only fly bigger planes for KLM but also the new Boeing Business Jet that has been ordered by the Dutch government to replace the existing royal/ government plane, a Fokker 70.
De Telegraaf has an interview with the King but as it is a premium article, I don't have access to the entire interview. Perhaps some other Dutch poster has.