For a flat roof especially one you intend to walk on (!) shingles will not fly. They are not meant to be walked on and it will likely void any warranty. Also flat roofs themselves do not work with shingles - they are designed for a roof with a pitch. To shed water here you will likely need rubber membrane. But I would not allow foot traffic on this surface period.

thanks i likely needed to be more specific this are slate deck tiles.

we do have a rubber membrane down and they would go over it

12"x12" SuperWood Deck Tiles, Composite Walnut, Snap To Install · More Info

Interlocking slate deck tiles on patio · More Info

The rubber tiles will be better for shedding water. The interlocking tiles are meant to go over a solid surface (like concrete) to lay flat properly. These will collect and hold water on the surface also whereas the rubber tiles should have grooved channels on the underside.