The Targeted Free Energy Perturbation (TFEP) method aims to overcome the time-consuming and computer-intensive stratification process of standard methods for estimating the free energy difference between two states. To achieve this, TFEP uses a mapping function between the high-dimensional probability densities of these states. The bijectivity and invertibility of normalizing flow neural networks fulfill the requirements for serving as such a mapping function. Despite its theoretical potential for free energy calculations, TFEP has not yet been adopted in practice due to challenges in entropy correction, limitations in energy-based training, and mode collapse when learning density functions of larger systems with a high number of degrees of freedom. In this study, we expand flow-based TFEP to systems with variable number of atoms in the two states of consideration by exploring the theoretical basis of entropic contributions of dummy atoms, and validate our reasoning with analytical derivations for a model system containing coupled particles. We also extend the TFEP framework to handle systems of hybrid topology, propose auxiliary additions to improve the TFEP architecture, and demonstrate accurate predictions of relative free energy differences for large molecular systems. Our results provide the first practical application of the fast and accurate deep learning-based TFEP method for biomolecules and introduce it as a viable free energy estimation method within the context of drug design.