Fall (slope) on a 'flat' roof should be built into the timber, the felt is only a waterproofing layer. I suspect it would be difficult to build a fall into an additional layer of felt, unless the higher end was built up with several layers of felt, reducing to a single layer at the lower end. If you are to relay, I'd go with your idea to slope towards the foreground in the pic, and fit a gutter across the fascia there to collect the runoff.
Normal practice is to spread white stone chippings over the finished roof to reflect the sun and protect the felt. (Looks like this has been done on the section to the right, just as it goes out of shot?)