I've been drying my fiber prints using one of those ferro-type/canvas dryers and have been happy getting flat prints. Just for the hell of it I wanted to try air drying. I don't have screens so I squeegeed the prints on each side and placed them face down on my bedroom carpet which has a medium pile height. To be safe I have a real good vacuum and cleaned the area real well. After about an hour or so I gently picked up the prints and put them down again just to make sure they didn't stick to the carpet. (they didn't). Much to my surprise in the morning I had perfectly flat prints. They were even very slightly flatter than those I dried in the dryer.
I dried half the prints in the dryer and half on the carpet. One thing I think I noticed is that the dryer prints seemed to have very slightly blacker blacks. and possibly had more of a dry down effect like maybe 1 or 2 %.