Removing Fleck Stone from wooden desk?

I would experiment with paint remover - Nitromors type shifts most things. If it is not in too bad condition sanding it might be the best option - it is a cellulose type base so be careful not to breathe in the dust. (Acetone might work as an alternative solvent). Sanding will give a good key then I would prime with good quality oil based undercaoat and coloured top coat and finish with varnish if you are doing the decoupage thing.