Fluxon dynamics in a system of three coupled driven damped sine-Gordon equations is investigated. Bunching of fluxons is observed. It is shown that fluxon-fluxon-fluxon bound states exist in a certain interval of the fluxon velocity. Attraction between fluxons occurs as a result of indirect fluxon-fluxon interaction mediated by Swihart waves. To tackle the problem analytically a piece-wise linear approach is developed. The analytical approximations show good agreement with the results obtained by direct numerical simulations.