From my vast knowledge of drying timber, gained by watching many episodes of Grand Designs, drying wood in a kiln can dry it too quickly, and cause it to split. Maybe not now, but in years to come. Apparently it’s much better to let it air dry naturally.
As a land surveyor I’ve referee’d many property line disputes. Generally, the guy paying, i.e. you, gets to choose the orientation of the flat side. This is a general courtesy and not legally binding. If your neighbor has any qualms tell him he may board his side of the fence to his liking, as long as he pays for it and doesn’t fuck shit up.