Hi Silloh,
You can use the quest API to retrieve a quest by ID, and then lookup the other quests in the chain by accessing the data for the quests “category”.
https://us.api.blizzard.com/data/wow/quest/57220?namespace=static-us&locale=en_US&access_token=TOKEN
Leads to:
https://us.api.blizzard.com/data/wow/quest/category/584?namespace=static-us&locale=en_US&access_token=TOKEN
I hope this helps.