Do you plan to make just one chair, or do you want to mold them in quantity?
If you want to make just one chair (maybe for your personal use) your best source of information probably will be on websites devoted to model airplanes/rocketry or homebuilt aircraft. They build curvaceous designs using epoxy resin and fiberglass/kevlar/carbon fabrics, but without the need or expense of molds. You can adapt their techniques and sustitute carbon fiber cloth wherever they call for fiberglass or kevlar. They also will point you to materials suppliers.
If you plan to make a mold and produce chairs from the mold, you'll need a lot more information to do this work in a professional manner. You could try to obtain the knowledge on your own, but plan on spending quite a bit more than if you hired a professional in the trade to build the mold(s) from your design.