When I wash my fabric, I take it out of the washing machine, shake it intil it is fairly straight or lay it out on a table or the top of my freezer and smooth it flat, and then I hang it up on hangers to dry. Might take a little while, depending on your climate, but I live in AZ - it's dry in less than hour if I hang it outside in the summer. I use skirt hangers to dry fat quarters (3 to a hanger) or about a yard of fabric. I use the big plastic hangers to dry lengths of fabric larger than a yard - just fold it in half and slide it onto the hanger.
Drying it hanging tends to flatten out the fabric and it needs very little pressing. Can store it folded without ironing until needed without a lot of lumps.