Magnetic colloidal chains are a microrobotic system with promising applications due to their versatility, biocompatibility, and ease of manipulation under magnetic fields. Their synthesis involves kinetic pathways that control chain quality, length, and flexibility, a process performed by first aligning superparamagnetic particles under a one-dimensional magnetic field and then chemically linking them using a four-armed maleimide-functionalized poly(ethylene glycol). Here, we systematically vary the concentration of the poly(ethylene glycol) linkers, the reaction temperature, and the magnetic field strength to study their impact on the physical properties of synthesized chains, including the chain length distribution, reaction temperature, and bending modulus. We find that this chain fabrication process resembles step-growth polymerization and can be accurately described by the Flory-Schulz model. Under optimized experimental conditions, we have successfully synthesized long flexible colloidal chains with a bending modulus, which is 4 orders of magnitude smaller than previous studies. Such flexible and long chains can be folded entirely into concentric rings and helices with multiple turns, demonstrating the potential for investigating the actuation, assembly, and folding behaviors of these colloidal polymer analogues.