Source

Dropped by Nightbane, a secret boss in the Return to Karazhan dungeon on Mythic difficulty. This mount has a quite high drop rate (20% if solo). This scales and increases with the number of players in the group, up to 100% drop rate for a full group of 5 players.

How to get the Smoldering Ember Wyrm?

Nightbane is the secret (and final) boss in the Return to Karazhan dungeon on Mythic difficulty.

Upon entering the dungeon, you will see a message in the chat log that says "The strange chill of a dark presence winds through the air." If the message doesn't appear, it is likely that you're on the wrong difficulty.

Message in the chat log when entering the Return to Karazhan dungeon on Mythic difficulty

Once you see the message, you can proceed through the dungeon as normal. While progressing, you will encounter 5 crystals called Soul Fragment that you need to interact with. These crystals gives you a buff called Medivh's Echo that stacks. At 5 stacks of the buff, it becomes Medivh's Presence. Do not die during this run, as you will lose all your stacks and have to start over.

1. The first crystal is located in the first boss room: The Opera. Kill the boss and go to the spectator area (in the opposite stage) to find the crystal in the middle of the room. Click on it to get the first stack of Medivh's Echo. You can see that the buff has a timer of 10 minutes, but each crystal you interact with adds 5 minutes to it.
2. After the Opera, exit its hall behind the crystal and head towards the Maiden of Virtue wing. When you enter the Banquet Hall, take the left door. When you're on The Guest Chambers, take the left door right before the Maiden of Virtue boss room. Take out any trash mobs in the room and you will find the second crystal at the back of the room, on the left side. Click on it to get the second stack of Medivh's Echo.
3. For the third crystal, head back the way you came and jump down into Moroes' room. Kill the boss, and the crystal will appear right behind him.
4. Let's see some spiders. From where you picked up the third crystal, turn around go to the room on the left, where you can see an Elemental. One you went though the pillars, go directly to the right and take the stairs down. While you're here, you can have a chance to get the Midnight's Eternal Reins, which is a rare drop from Attumen the Huntsman. This mount is the updated version of the Firery Warhorse, from the original Karazhan dungeon. Once you finished in the stable, go to the Servant's Quarters and take the door on the back of the room. Then, follow the path to the red mark:
   Location of the fourth crystal
5. One you interacted with the fourth crystal, you can take the portal right behind it. You will be teleported back to the entrance, but this time you need to take the right path, to the Menagerie where The Curator is. Kill the boss and the fifth crystal will appear right underneath him. Once you have the fifth stack of Medivh's Echo, your buff will turn into Meidvh's Presence. You will have 5 minutes to go speak with Medivh and summon Nightbane.
6. When the buff is active, go back to where you came from, drop down from the broken stairs to save a bit of time, you will be at the entrance again. Take the same path as before, but this time, don't go up the ramp, take the small open door under said ramp. You'll find the Image of Medivh there. Interact with it and it will summon Nightbane. Kill the boss and hope for the mount to drop!