Use a cation exchanger (especially SCX) to retain amino acids and wash out the chloride ions...Carefully dilute and adjust pH to retain all amino acids
For large-volume applications, you may prefer batch-mode purification. Add the prequibilirated bulk resin into the sample and incubate for a while and shake continuously. AAs will adsorb on resin while Chlorides are not.
If the purpose is just analysis, you can derivate the AAs and LLE using organic solvents such as ıso-octane, chloroform, acetonitrile, MTBE, etc may give a chance of both chloride removal and enrichment of the AAs.