I saw King Crimson as an opening act when their first album came out and was blown away. That is indeed a flute, played by sax and woodwind player Ian MacDonald. He did also play keys including mellotron, but I clearly remember him playing the flute in that song.
Thank you for clarifying that. I always thought that sounded too realistic to be some synthetically produced noise, but, not being a musician, I didn’t know. That song brings me to a peaceful plane whenever I think about it, including the sound of the Cymbal being struck or brushed at the end of the measures.