I listened to In Search of the Lost Chord on Tuesday, and then I learned the flute parts from ~1:55 to ~2:09 in "House of Four Doors (Part 1)."
The left-channel flute is something like:
While playing this over, the intervals seemed familiar, and I realized that - perhaps coincidentally - they're exactly the same as the last few measures of the first section of "Greensleeves":