Personally I have a love/hate relationship with Kilim. Love it for rugs (don’t forget your rug pad, they will slip!), Love it for footstool covers, Love it for wall hangings. Not so sure about for pillow covers. Why? Because while they look good, and are textural, often colorful and interesting to look at, they are NOT face-friendly.
So please proceed to use Kilim pillow covers for the seating that you only sit on, or look at, but don’t use it for the sectional sofa you lie all over at night to watch your favorite TV shows. For detailed information about Kilim please click on the Wikipedia definition. I promise you will learn more than you thought possible about Kilims; I know I did.