Cannot Start Work Order for Seal of Broken Fate

The free Seal of Broken fate counts toward the three purchase-able seals players can obtain each week. If you have already purchased three seals from the vendor in Dalaran, you will not be able to complete the quest for one free seal during the week.

You will also not be able to complete the quest if you haven't completed the Order Hall Advancement in eligible classes Class Halls. 

Here is a list of the quests that grant one free seal, by class:

Demon Hunter: Fate Favors Us
Druid: Essence of Fate
Hunter: Unseen Fate
Mage: Fate and Time
Monk: Meditations on Fate
Paladin: Fate's Blessing
Priest: The Fates Bless Us
Rogue: Seal Their Fates
Shaman: Shape Your Fate

Death Knights, Warlocks, and Warriors don't have an option to research work orders for Seals of Broken Fate weekly from their Class Order Hall.

Note that additional Seals of Broken Fate obtained from missions do not count toward the 3 purchasable in Dalaran. Players may have up to 6 Seals of Broken Fate at a time.