Washing, drying, and ironing fabric is really a drag. However, if you get a supply of skirt hangers (the hangers with two clips for pants and/or skirts), you can wash your fabrics, then hang it up. It will dry almost flat (at least flat enough not to have to iron it until you get ready to cut it). A three yard piece of fabric will hang really well on a skirt hanger without a problem.
I wash multiple fat quarters in a lingerie bag. These I also hang on hangers and dry flat. You can clip three or four fat quarters on one hanger and they will dry fairly quickly. Also will be almost flat.