Fan fluting looks like a row of parallel channels. It is not - every channel is a different length, and each one tapers, and that is what makes it difficult.
The flutes radiate from a point low in the back and spread as they rise, so each channel is narrow at its foot and wide at its head. If the wadding inside them were cut as uniform strips, the narrow ends would be over-filled and stand proud while the wide ends would be under-filled and read flat. The fan would appear to swell in the middle and die at the edges.
So the filling for every channel is cut individually, tapered along its length to match the channel it goes into - thinner where the flute is narrow, fuller where it opens - so that the height of the relief stays constant from the bottom of the fan to the top.
The velvet is then worked into each channel one at a time, always in the same direction, so the pile lies the same way across the whole back. Velvet worked in alternating directions would read as alternating light and dark stripes, and no amount of good fluting would rescue it.