Right, it's definitely overcoat weather now. It is always cut to be worn over the coat beneath. It is worn with both day and evening formal dress i.e. morning coat, or evening dress coat (white tie). It may also be worn with a dressier lounge suit for city wear, but that is about as casual as the dress may be under a Chesterfield.
It always has flap pockets, and definitely always single vents. Double vented overcoats are very much a thing of the past, when they did once make double breasted paletots and paddock coats that way. Chesterfields were never made with double vents.