Head north from the Fort Arand Wayshrine. The entrance to Emberflint Mine is in the tunnel that leads the public dungeon. There are two ways you can use to enter the same tunnel, and both of them lead to the Emberflint Mine door.
Further into the dungeon, you’ll get to the first large room. Keep to your right and enter the tunnel on the same side (not left). This path will take you to the higher dungeon platform. At the end of it is the small bridge with the shard on it.
Tunnel entrances that lead toward Emberflint Mine door.
Emberflint Mine Door.
Emberflint Mine Door Map Location.