With the way all the cats I know loving quilts the way they do, the cats just may take over any quilted items! I wonder if there is a textured material that the cats would not like the feel of and leave alone?
If I were making something to protect the chair arms that I knew would be getting destroyed by cats, I would choose a simple 4P with larger squares separating the 4Ps that I could machine applique on as necessary and just plan on replacing the whole thing at least once a year.