Temperature- and frequency-dependent infrared spectroscopy identifies two contributions to the electronic properties of the magnetic kagome metal Fe_{3}Sn_{2}: two-dimensional Dirac fermions and strongly correlated flat bands. The interband transitions within the linearly dispersing Dirac bands appear as a two-step feature along with a very narrow Drude component due to intraband contribution. Low-lying absorption features indicate flat bands with multiple van Hove singularities. Localized charge carriers are seen as a Drude peak shifted to finite frequencies. The spectral weight is redistributed when the spins are reoriented at low temperatures; a sharp mode appears suggesting the opening of a gap due to the spin reorientation as the sign of additional Weyl nodes in the system.