We consider the Langevin dynamics of a semi-dilute system of chains which are random polyampholytes of average monomer charge q and with fluctuations in this charge of size Q(-1) and with freely floating counter-ions in the surrounding. We cast the dynamics into the functional integral formalism and average over the quenched charge distribution in order to compute the dynamic structure factor and the effective collective potential matrix. The results are given for small charge fluctuations. In the limit of finite q we then find that the scattering approaches the limit of polyelectrolyte solutions.