How do I stop my recliner from scratching wood floor
Does the recliner have distinct "feet" under the disk? 

If so, some rubber floor protecting pads under those feet should stop the scratches and the sliding:



(this one is just a representative sample, they come in many shapes, sizes, and materials)

If the entire disk contacts the floor, then how about just putting a carpet under it (with a non-slip pad under the carpet)