Summary: We consider Einstein Born-Infeld theory with a null fluid in Kerr-Schild geometry. We find accelerated charge solutions of this theory. Our solutions reduce to the Plebański solution when the acceleration vanishes and to the Bonnor-Vaidya solution as the Born-Infeld parameter \(b\) goes to infinity. We also give the explicit form of the energy flux formula due to the acceleration of the charged sources.