I've polished some seatposts by hand to a mirror finish this way:
1) Mount the seatpost without saddle in the frame, about 5 mm higher than it will be when finished. Place a big rubber or plastic washer over the seatpost to protect the frame.
2) Cut long strips of wet or dry sandpaper and put one round the seatpost, support the rear wheel with your knees and work the sandpaper back and forth, evenly. Avoid staying in one place, cover all surface. I started with #320 and continued with #600 grit sandpaper. Continue until the machining marks are gone.
3) Cut rag strips about 30 cm long and work in the same way as before, with polishing paste. I used water to 'thin' it.
4) Same as #3 but with auto polishing compound.
5) Same as #4 but with clean rag.
Note: The seatposts I polished were solid round, possibly with a fluted one you have to be extra careful so as to keep the fluting edges sharp.