Welcome from Nevada!
That's an awesome looking body pillow case! What's so much fun about it is that you can pick out any color, or collection of colors, to make it from. You could coordinate with your current bedspread. Or use it as an accent. Or coordinate with something else in the room. I think it's meant to be quilted (yes? No?) A simple flannel back would be perfect. I don't think you'd want batting. And then a simple "stitch in the ditch" (SITD) should be sufficient, and really make those blocks stand out, plus add some strength to the case. If I were making this, I'd made a backing that looked like another pillow. You could do that easily with stripes. The stripes could be wide -- take with needed width and length of the back. Divide the width by however many stripes you want. You could make the stripes 5-6 inches wide, or even wider, and just longer than the pillow. Sew together. Cut to fit backing. Voila! Second pillow. Little effort. Or sew together equal sized blocks for the back. A little less showy, but still a very nice backing that no one would ever take for a backing.
Just a thought.
Warmest Welcome to the Quilting Board. Glad to have you aboard!