the flashing looks untidy, but I honestly think it would look neatest, and the results longer-lasting, if you applied a trim piece, such as a white PVC moulding, onto the edge of the roof. I suppose it is about 75 or 100mm.
If you can find a roofer willing to do such a small job, there is probably something suitable used for edges of flat roofs such as car ports. You could fix it yourself if the roof is made of wood, taking care to put the screws where water will not track inside, and avoiding the flashing.
You could use wood trim, but it would soon rot.
If the roof is a thin reinforced concrete slab, be sure to use plasplugs and stainless steel screws. Rusty screws in such a thin section would crack it.
I don't think your stone chippings would adhere for long on that edge.