The vibrational modes in organic/inorganic layered perovskites are of fundamental importance for their optoelectronic properties. The hierarchical architecture of the Ruddlesden-Popper phase of these materials allows for distinct directionality of the vibrational modes withrespect to the main axes of the pseudocubic lattice in the octahedral plane. Here, we study the directionality of the fundamental phonon modes in single exfoliated Ruddlesden-Popper perovskite flakes with polarized Raman spectroscopy at ultralow-frequencies. A wealth of Raman bands is distinguished in the range from 15-150 cm-1 (2-15 meV), whose features depend on the organic cation species, on temperature, and on the direction of the linear polarization of the incident light. By controlling the angle of the linear polarization of the excitation laser with respect to the in-plane axes of the octahedral layer, we gain detailed information on the symmetry of the vibrational modes. The choice of two different organic moieties, phenethylammonium (PEA) and butylammonium (BA) allows to discern the influence of the linker molecules, evidencing strong anisotropy of the vibrations for the (PEA)2PbBr4 samples. Temperature dependent Raman measurements reveal that the broad phonon bands observed at room temperature consist of a series of sharp modes, and that such mode splitting strongly differs for the different organic moieties and vibrational bands.