After defeating the Jade Oni, you should get the spiral key from the Emperor of Mooshu and he'll send you back to Merle Ambrose. (Quest name: The Key at Last)
Next, Merle will have you go talk to Cyrus Drake. Cyrus wants to make sure you're ready for the challenge ahead of you. (Quest name: Bad Blood)
Once he's satisfied you can handle yourself, Cyrus sends you to Dragonspyre. (Quest name: Crystal-Matic)
If none of these has come up for you, make sure you spoke to the Emperor of Mooshu after defeating the Oni. He'll be standing on the platform behind the battle circle.
If you've done the quest The Key at Last (which is given by Emperor Yoshihito after defeating the Jade Oni and ends with you talking to Headmaster Ambrose) and if you've done the quest Bad Blood (Which directly follows The Key at Last, it is given by the Headmaster, during which you fight Cyrus and afterwards meet him in the Basilica) then you should be in Dragonspyre.
However I do know of certain bug that has caused me to "misplace" my Spiral Keys, (at least the one for Dragonspyre) the last time I saw that bug I was in a similar situation to yours but for some reason Dragonspyre wouldn't appear as an option when I interacted with the Spiral Doors. Idk if that bug interferes with the quest progression or just the doors. The problem may or may not be the same.
If you can't find the reason in game I would go back out to the main page click the "Help & Support" tab at the bottom then click "Contact Support" and explain the problem to them in detail including the name of the character the problem is on, etc...
Hope this helps, hopefully you'll be adventuring in Dragonspyre soon!