A series of main-chain poly(amide-triazole)s were prepared by copper(I)-catalyzed alkyne–azide AABB-type copolymerizatons between five structurally similar diacetylenes 1–5 with the same diazide 6. The acetylene units in monomers 1–5 possessed different degrees of conformational flexibility due to the different number of intramolecular hydrogen bonds built inside the monomer architecture. Our study showed that the conformational freedom of the monomer had a profound effect on the polymerization efficiency and the thermoreversible gelation properties of the resulting copolymers. Among all five diacetylene monomers, only the one, that is, 1-Py(NH)2 which possesses the pyridine-2,6-dicarboxamide unit with two built-in intramolecular H bonds could produce the corresponding poly(amide-triazole) Poly-(PyNH)2 with a significantly higher degree of polymerization (DP) than other monomers with a lesser number of intramolecular H bonds. In addition, it was found that only this polymer exhibited excellent thermoreversible gelation ability in aromatic solvents. A self-assembling model of the organogelating polymer Poly-(PyNH)2 was proposed based on FTIR spectroscopy, XRD, and SEM analyses, in which H bonding, π–π aromatic stacking, hydrophobic interactions, and the structural rigidity of the polymer backbone were identified as the main driving forces for the polymer self-assembly process.