Vaccines work by training immune cells to recognize a certain pathogen and activate a powerful secondary immune response to defeat that pathogen. These immune cells are already present in the individual and, in the absence of any immunological disorder, are not the limmiting factor when the body combats an unidentified pathogen.
Therefore, cloning the immune cells of a specific person and inserting these untrained immune cells into an individual would not provide any significant benefit against infection or boost immunity. Inserting immune cells that had been trained to recognize a pathogen would work, but vaccination is a much easier and cheaper method to achieve the same result.