I read on wowhead that it’s an eventual part of the chain involving the new ‘ring’ quest chain, and that flying only works outside of storms.
Here’s the actual info:
During your time in Siren Isle, you will go through a couple quests to earn upgrades for your Cyrce’s Circlet. The last quest in the chain, Cyrce Would Be So Proud, teaches you how to master the strong winds of Siren Isle, and finishing this quest will allow you to fly in Siren Isle while it’s not storming!
Unfortunately for those who want to fly, you will still be grounded in Siren Isle while a storm is going on due to Seafury Tempest - As of right now on the 11.0.7, you can choose whether you go into a storm or not (but there are different objectives and enemies while a storm is going on in Siren Isle).