Oh, gee. Call the airline, but I really don't think you can check it free. It's not nearly the same as a stroller or car seat.
Also, any checked item over 62 linear inches (length + width + depth) costs $100 to check. I don't know if a folded pack & play is larger or smaller than this.
It'll be easier and less stressful, and probably cheaper, to just rent one from A Baby's Best Friend abbf.com. They're reputable, and they'll deliver and pick up.