Why don't free amino acids have peptide bonds? What is a free amino acid exactly?

Free amino acid do not have a peptide bond, as the amino acid act as a monomer which multiplies and linked via peptide bond to generate protein chain.

A free amino acid have a carbonly group ( - COOH) and a - NH₂ group.

The formation of protein chain require at least two amino acids linked via peptide chain.

The role of peptide chain only comes in case of protein, because it acts as a linking species.

Hence, free amino acid does not have any peptide chain.