We report an inelastic neutron scattering study of coherent magnetic excitations in powder and single-crystal samples of the model kagome antiferromagnet potassium iron jarosite, KFe3(OH)(6)(SO4)(2). Initial measurements on a natural single crystal using a triple-axis spectrometer revealed a mode with a zone-centre gap of 7 meV that showed little dispersion within the kagome layers, as well as some indication of a mode with a zone-boundary energy of approximately 20 meV. However, the high background from hydrogen in the sample made it very difficult to search for other excitations. In the absence of suitable deuterated crystals, measurements were performed on deuterated powders using time-of-flight neutron spectrometers over a range of temperatures that include T-N congruent to 64 K. This confirmed the flat 7 meV mode as well as dispersive modes that reached to higher energies. The origin of these modes is discussed in relation to the most likely Hamiltonian for the magnetic degrees of freedom in this material, and estimates are made of the strength of the nearest-neighbour exchange, J(1), and contributions from a Dzyaloshinsky-Moriya interaction or single-ion anisotropy arising from a crystal field.