The attractive interaction in conventional BCS superconductors is provided by a bosonic mode. However, the pairing glue of most unconventional superconductors is unknown. The effect of electron-boson coupling is therefore extensively studied in these materials. A key signature is dispersion kinks that can be observed in the spectral function as abrupt changes in velocity and lifetime of quasiparticles. Here, we show the existence of two kinks in the unconventional iron-based superconductor RbFe2As2 using angle-resolved photoemission spectroscopy (ARPES) and dynamical mean field theory (DMFT). In addition, we observe the formation of a Hubbard band multiplet due to the combination of Coulomb interaction and Hunds rule coupling in this multiorbital system. We demonstrate that the two dispersion kinks are a consequence of these strong many-body interactions. This interpretation is in line with a growing number of theoretical predictions for kinks in various general models of correlated materials. Our results provide a unifying link between iron-based superconductors and different classes of correlated, unconventional superconductors such as cuprates and heavy-fermion materials.