Turns out flying might be possible on the Siren Isle after all, with Wings of the Siren suggesting that the Cyrce's Circlet may be the key.
Although we don't know exactly if or when flying will be unlocked, there are also other options for getting around the island, such as the Experimental Go-Pack: rocket assisted jumps which allow you to glide through the air!
Siren's Isle No-Flight Mechanics and Size As of the first Patch 11.0.7 PTR build, there are two debuffs in Siren Isle that restrict flying: The first one is the previously reported High Winds, which is enabled at all times in Siren Isle.
Once a storm event is started in Siren Isle, a second debuff shows up, Seafury Tempest, further emphasizing high winds making flight difficult on the isle.As of this PTR build, you're able to speak to an NPC and «choose» whether you want to be in a storm or not.
Siren Isle during Seafury Tempest has different objectives and is overall more challenging, with many elite mobs and stronger rares.