What will happen if you put jeans in the dryer that say dry flat?

If you don't follow the directions and dry them flat, they will more than likely shrink unevenly and the fabric may pucker up. You may be able to rescue the wrinkly fabric with an iron, but if the jeans shrink unevenly, you're out of luck unless you are an expert sewer who can pick open the seams, realign the fabric and then sew them back together. Of course, these disasters may not happen at all, but its better to follow the directions and be safe not sorry.