It appears you don’t need to complete the Battle for Azeroth Pathfinder to fly in Kul Tiras and Zandalar in Dragonflight.
Battle for Azeroth becomes two expansions old with Dragonflight and when Shadowlands was released, Blizzard made Warlords of Draenor flying available to everyone with the Pathfinder still rewarding the mount.
On the Dragonflight Beta, we tried flying in Zuldazar on a character that has never unlocked Battle for Azeroth Pathfinder, Part Two and it worked, even though the achievement still says it rewards flying.
The achievement will most likely only award Wonderwing 2.0 in the Dragonflight pre-patch.
