Despite reading the available papers about ATAT and the manual I still can’t find detailed information about the method of calculating phonon properties. But from what I have read I am guessing it is the finite difference method since perturbed supercells have to be generated. Can I also use the linear response method as implemented in VASP? And if so how can I then extract the data nessecary for ATAT?
No, atat does not process linear response data (there are other codes that do that already - e.g. phonopy).