Can you be more specific about the membrane to use and 2" of foam insulation? Something I can suggest to a flat roof specialist. Thanks.
Membrane roofs are exterior vapor barriers, so the foam helps protect the roof deck & rafters from rot by keeping it above the dew point of the inteior space air in winter, avoiding condensation at the roof deck, making it resilient to air leaks from the conditioned space. But the amount of foam required is climate-dependent, as well as the R value of the insulation in the rafter/joist bays.
The dew point of 70F 35% relative humidity air is about 40F, so if you keep average temp at the structural roof deck in January stays above 40F with a 70F interior it's enough prevent moisture accumulation at the roof deck. In say, Gaithersburg the outdoor mean temp for January is ~30F so if you have R30 batts or cellulose in the rafters/joists (2x10s, nominally), you need at least R10 in foam above the roof deck to prevent condensation. That would take 2.5" of EPS (bead-board), or 2" of XPS (extruded polystyrene), or 1.5" of polyisocyanurate. In Baltimore the mean January temp is ~35F, so with R30 in the rafter bays you'd only need a minimum of ~ R5 above the roof deck, so 1.5" of EPS or 1" of XPS or 1" of iso would be enough, but you'd have more margin with 2".
If you had R38 in the rafter bays (2x12s), that's about 25% more R, so you have to scale up the foam by ~25% (3" of EPS or 2.5" of XPS/iso for Gaithersburg, or 2" EPS or 1.25" of XPS/iso in Baltimore.)
If the rafter bays are empty or don't have full depth batts/blown fiber, measure the full cavity depth and multiply by 3.5" to come up with a number to approximate a full fill of cellulose for calculating your foam-R, then retrofit it with cellulose. That way convection loops impede any interior air from finding it's way to the roof deck in the first place, and during the hours where it's colder than 30F outdoors and potentially condensing at the roof deck, any condensation that forms is wicked up & safely redistributed by the cellulose to dry seasonally toward the interior. If you don't want to mess up the interior with blowing holes it can be drilled & filled from above prior to laying down the rigid foam.