The Ethereal Fluke can be found in the Dream World, which is only accessible during Lunar Diplomacy.
The Ethereal Fluke directs one of the tasks the player must complete in the dream section of the quest. In "A game of chance," the Fluke shouts out a number, and the player flips over dice till the numbers facing up on the dice equal the Fluke's number. The character's examine text refers to this.
