The design will not stand the test of time. Your reservations about flat roofs are well-founded. I suggest that you look at Houzz pages of local architects in the Pacific Northwest, particularly those who have won awards from their peers.

A lot of modern builds will have flat roofs in some part of the home it's how it's designed and how the roof is installed which will make it last .

Whoa, don't throw the baby out with the bathwater. This basic elevation has promise but the rooflines need work. Maybe use low slung hipped roof lines; Ledgerton Architecture and Gelotte Hommas both have good designs on Houzz that can help and Kevin Akey at AZD Architecture has a really good grasp of the Prairie style roof. You could also try a different take on the shed roof, the Cattlemen's Club House is a project on Houzz with some inspiration or The Ryan Group has a design that could inspire a shed roof concept. For what its worth, Rockin' Fine is right, there is nothing wrong with flat roof's if they are insulated and finished correctly, beware of skimping on the membrane.