T.S.
H.,
I can't answer your question, but we had a new roof put on our entire home in December, including the flat roof portion of the house. We did gwt some sort of rubber roof. Perhaps you should get another 1 or 2 estimates from recommended roofers, and when you are speaking with them, after they tell you what to do on the flat roof part, be frank with them and say another contrator recommended (whichever type the one you're talking with didn't) and see what the differences are. Our contractor was going to put a different type of roof on but then decided on the rubber roof.
Good luck! It can be really aggravating dealing with home improvement issues when the estimates are not for the same thing! Been there, done that!