Destructive interference of electron hopping on the frustrated kagome lattice generates Dirac nodes, saddle points, and flat bands in the electronic structure. The latter provides the narrow bands and a peak in the density of states that can generate correlated electron behavior when the Fermi level lies within them. In the kagome metal CoSn, this alignment is not realized, and the compound is a Pauli paramagnet. Here we show that replacing part of the tin with indium (CoSn1−xInx) moves the Fermi energy into the flat band region, with support from band structure calculations, heat capacity measurements, and angle resolved photoemission spectroscopy. The associated instability results in the emergence of itinerant antiferromagnetism with a Neel temperature up to 30 K. Long range magnetic order is confirmed by neutron diffraction measurements, which indicate an ordered magnetic moment of 0.1-0.2 µB per Co (for x = 0.4). Thus, CoSn1−xInx provides a rare example of an itinerant antiferromagnet with a small ordered moment. This work provides clear evidence that flat bands arising from frustrated lattices in bulk crystals represent a viable route to new physics, evidenced here by the emergence of magnetic order upon introducing a non-magnetic dopant into a non-magnetic kagome metal.