Put down drop cloths on a floor in a well-ventilated area, like a garage or shed. Place your Panton chair on top of the drop cloths.
Put on safety glasses, a dust mask and rubber gloves.
Dampen wet/dry sandpaper liberally with liquid sander, then abrade the Panton chair, sanding away the old peeling paint. You are not trying to remove all the paint, because it will be infused into the plastic; you are only removing flaking paint and roughing the surface.
Wipe the entire Panton chair down with tack cloths to get any dust off the chair once well-sanded. Then rinse with plain warm water and allow to air dry.
Spray an even coat of aerosol plastic-adhesion primer over the Panton chair and let dry as long as directed by the manufacturer. Be sure to cover the entire chair, flipping or tilting it when necessary.
Apply a coat of plastic aerosol paint once the plastic-adhesion primer is completely dry. Let the first coat dry according to the manufacturer's suggested drying time, then spray on a second coat. Spray on a coat of plastic-flex agent and let dry to finish repainting your Panton chair.