Exterior foam can reduce air leaks limit condensation at the sheathing layer interrupt thermal bridging through the rafters and make ice dams unlikely.
Unvented cold deck flat roof.
The higher the interior moisture level the thicker the rigid insulation required.
However in many situations the insulation may need to be primarily or entirely below the flat roof membrane and between the roof joists if so what are the best options.
Unvented flat roofs a technical discussion flat roofs have often been built with the insulation all on top of the vapor closed drainage plane as this avoids dew point condensation issues inboard of the roofing.
In unvented roof assemblies the thermal moisture and air control boundaries are moved to the roof deck so that the attic space is at the same condition as the living space and air movement between the two does not contribute to energy waste occupant discomfort or contaminant problems.
Where the insulation is placed above the structural deck warm deck and either above or below the waterproofing.
There is no need for additional ventilation.
Unvented flat roof assembly.
It is universally recommended that cold deck flat roof construction should be avoided.
One of the best ways to insulate a roof whether sloped or flat is to install rigid foam on top of the roof sheathing.
Drying of unvented roofing assemblies is by definition only provided to the interior.