While robotic automation has demonstrated remarkable performance, such as executing hundreds of experiments continuously over several days, designing synchronized motions between the robot and experimental jigs remains challenging, especially for flexible experimental automation. This challenge stems from the fact that even minor changes in experimental conditions often require extensive reprogramming of both robot motions and jig control commands. Previous systems lack the flexibility to accommodate frequent updates, limiting their practical utility in actual laboratories. To update robotic automation systems flexibly by chemists, we propose a concept that enables the automation of experiments by utilizing dual demonstrations of robot motions and jig operations by chemists. To verify this concept, we developed a chemical-experiment-automation system consisting of jigs to assist the robot in experiments, a motion-demonstration interface, a jig-control interface, and a mobile manipulator. We validate the concept through polymer-synthesis experiments, focusing on critical liquid-handling tasks such as pipetting and dilution. The experimental results indicate high reproducibility of the demonstrated motions and robust task-success rates. This comprehensive concept not only simplifies the robot programming process for chemists but also provides a flexible and efficient solution to accommodate a wide range of experimental conditions, providing a practical framework for intuitive and adaptable robotic laboratory automation. Our project page is available at: https://sasakihikaru.github.io/Chemical-Experiment-Automation-with-Dual-Demonstration/.