If you stop the dryer when the fabric is still a little damp before wrinkles are set, it should be a little easier to iron. If you can't get to them immediately, roll them up in plastic bags and freeze or they might get mildewed.
I'm paying attention here because I got a silly notion to machine embroider a set of 6 dish towels using some primitive looking fabric called Osnaburg, and I had the same problem. I was able to iron them flat, but feel as though I don't want to give them as a gift because as soon as they are washed again they will wrinkle, and I don't know anybody who will appreciate dish towels that need ironing. I'm seriously thinking of cutting out the embroidered areas and framing them. I would have done that by now, but I don't have the wall space and don't know anyone who would necessarily want such a design for their home. They would have been perfect in our first house in 1975, when everything was harvest gold and avocado green.
Here's what they look like, after ironing on the left and right out of the dryer on the right. The designs were from Embroidery Library.