We investigate the competing Fermi surface instabilities in the kagome tight-binding model. Specifically, we consider on-site and short-range Hubbard interactions in the vicinity of van Hove filling of the dispersive kagome bands where the fermiology promotes the joint effect of enlarged density of states and nesting. The sublattice interference mechanism devised by Kiesel and Thomale [Phys. Rev. B 86, 121105 (2012)] allows us to explain the intricate interplay between ferromagnetic fluctuations and other ordering tendencies. On the basis of the functional renormalization group used to obtain an adequate low-energy theory description, we discover finite angular momentum spin and charge density wave order, a twofold degenerate d-wave Pomeranchuk instability, and f-wave superconductivity away from van Hove filling. Together, this makes the kagome Hubbard model the prototypical scenario for several unconventional Fermi surface instabilities.