A simplified kinetic model scheme is presented that addresses the main reactions of two recently reported peptide self-replicators. Experimentally observed differences in the autocatalytic efficiency between these two systems-- caused by variations in the peptide sequences--and the possible effect of chiral amplification under heterochiral reaction conditions were evaluated. Our numerical simulations indicated that differences in the catalytic performance are exclusively due to pronounced variations in the rate parameters that control the reversible and hydrophobic interactions in the reaction system but neither to alterations in the underlying reaction network nor to changes in the stoichiometry of the involved aggregation processes. Model predictions further demonstrated the possible existence of chiral amplification if peptide self-replication is performed under heterochiral reaction conditions. Pointing into the direction of a possible cause for biomolecular homochirality, it was found that in open flow reactors, keeping the system under non-equilibrium conditions, a remarkable amplification of enantiomeric excess could be achieved. According to our modeling, this is due to a chiroselective autocatalytic effect and a meso-type separation process both of which are assumed to be intrinsic for the underlying dynamics of heterochiral peptide self-replication.