Use black automotive Goop from the backside if you want it to flex. It won't be like plastic welding but it is really good. Do several layers and let it set up between layers. I often use an old soldering iron first on the backside and Goop over the melted repair.
Plastic is polypropylene. Usually abbreviated with PP on underside. 3M, Norton, Pliogrip, Fusor all make a "plastic repair" material which covers PP. All of them will have a guide on how to repair cracks included with package. Best to use a mesh tape as a backing for strength.