How to reduce chair squeak
To find the exact spot where the squeak originates, use a meter-long piece of 3/4" heater hose or vinyl tubing. While you squeak the chair, your assistant uses the tubing like a stethoscope to find the loudest point under the chair.
Once you have found the point, mark it with a pen or chalk. It could be metal-to-metal, metal-to-plastic, or plastic-to-plastic. It could be in the center support, in an adjustment plate, or in the seat bottom or back.
You could spray something, rub a wax crayon, or sprinkle powder, depending on the exact location. Good luck, and keep trying.