A contractor told us it would be cheaper if we left the existing flat roof in place and then added the new pitched roof. Is this an advisable thing to do or is it a shortcut that we should steer clear of?
Depending on how your existing roof is structured it should be a very straight forward task.
Just as a mention, even flat roofs have a slight pitch.
Even pitched (gable) roofs start with the same structure at the ceiling level. Either one supporting wall is built slightly higher than the other, or by adding a little framing to create the slight pitch needed to get the rain off one side or the other.