Okay, so in order to unlock the class mount, you need to:
- complete order hall campaign
- complete legionfall campaign
- complete questline for class mount
For order hall campaign: Go here and look for the comment by Nalumis posted January 5th, 2017. Complete up to the achievement “A Glorious Campaign”
For legionfall campaign, here: You’re complete once you’ve gotten the achievement “Breaching the Tomb”
After you complete that, head back to Deliverance Point, and the quest “Worthy of the Title” will be available from Champion Cyssa Dawnrose to send you back to your class hall, to Lord Grayson Shadowbreaker. This is the actual quest that starts the mount questline.
The comment from Bursi on June 10th, 2017 lays out this questline.
Sometimes it doesn’t like to show up immediately, so you might have to fly to dalaran, /reload, or log in and out a couple times for it to pop up.
To easily check which quests you have completed on the lists, you can use this script in game:
/script print(IsQuestFlaggedCompleted(12345))
Replace the “12345” with the quest’s ID number, which can be found in the URL of each quest on wowhead. For example, the quest below “Warriors of Light”, the number is 43697. If the script comes back “True”, you have completed the quest. If “False”, then you have not.
https://www.wowhead.com/quest=43697/warriors-of-light
Edited to clarify and correct a couple things