I would use a styrofoam board like blue board. Just stick it between the rafters and call it a day. In your climate it should not cause any issues.
There are also reflective barriers you can put down under the shingles, don't waste your money. Put down a reflective type roof covering. The flat roof you are talking about should not be shingles. I would suggest a mulehide peel and stick, or a rubber membrane material. Both come in silver or white.