The flame transfer function (FTF) of an aeronautical burner in a rectangular combustion chamber is determined using large eddy simulation (LES). The configuration contains an industrial swirling device placed in a laboratory combustor. The swirler comprises three air passages and liquid kerosene is injected through a pilot and a multipoint injection device including 24 injection holes. In order to reduce computational costs, the forcing process for FTF determination is limited to three forcing cycles. Application of the dynamic mode decomposition (DMD) allows to extract the coherent flow structures at the forcing frequency and to construct local flame response and time delay fields. In a next step, modal analysis is carried out with a Helmholtz solver where acoustic boundary conditions are utilized taking mean flow effects into account. The latter allows to model mean flow effects in a zero Mach number framework. Results are compared with experimental observations: stable and unstable combustion modes for different outlet impedances are correctly identified by this methodology. All results are validated against experimental data and show good agreement.