The GDPR only applies to businesses, not individuals. So, clearly in this case it does not apply at all since the person behind @ElonJet is acting in an individual capacity.
The GDPR applies to everyone, except "by a natural person in the course of a purely personal or household activity", member states and some authorities.
the linking is done simply by looking up who the plane is registered to, and that is also public information.
you can of course always go the other way, look who owns a plane, and the go to flight information from there.
there is nothing private about any of the information used in the process.