I must say if I were flying LCY-EDI I can't think why I'd opt for FlyBe over BA. As already commented on, turboprops have less passenger appeal than jets. Also I presume the journey time will be longer so unless the price is significantly lower, which seems up unlikely I can't see how the route can work.
Given the competition on most of the other planned routes, albeit from other 'London' airports in most cases and on jet aircraft, FlyBe look like facing an uphill struggle with their LCY ops. I have to say, I find the choices made by the airline to be very strange.