A theoretical model for the radiation spectrum of an oscillator based on a flux flow through a long Josephson junction is considered. The broadening of the radiation linewidth due to nonperiodicity of a fluxon chain moving along the junction is found. The nonperiodicity arising due to intrinsic oscillations of the chain affected by the junction noise is treated in the white-noise approximation. At low noise the spectral line was found to have a Lorentz shape, the linewidth being proportional to the junction temperature.