I am certain these pillows will require frequent washings so a zipper was mandatory. I will sew a lapped zipper which has a pleat that covers the zipper and is stronger than an invisible zipper but, still looks good.
Directions for sewing a lapped zipper are included in the all purpose zipper package but, here are the steps. First machine baste the two pieces together that will have the zipper inserted. Use a generous 5/8" seam allowance and I also overlocked the edges before I basted the pieces together.
1. Carefully place the right side ( has the zipper pull ) of the zipper face down on one side of the seam allowance with the zipper teeth NEXT to NOT on the seam.
2. Using a zipper foot on the sewing machine sew the zipper to the one side of the seam allowance, and just the seam allowance. These stitches do not show on the front side of the fabric. Keep the zipper teeth next to the seam ( seam is what scissors are pointing at ).
3. Here's the confusing part. Fold back the side of the seam allowance that now has the zipper attached so the zipper is now right side ( see the zipper pull ) facing up. Carefully stitch in the folded back seam allowance between the zipper and the seam ( scissors are pointing to seam ). This is the step that creates the 'lap' in a lapped zipper.
4. Now the zipper is completely sewn to one side of the seam allowance and the other side of the zipper is not sewn to anything. Turn your entire fabric back right side up and stitch the fabric to the zipper side that is not sewn to anything. You can feel the zipper through the fabric but, ideally you are stitching about 1/4" from the seam ( where the scissors are pointing ).
5. CAREFULLY remove/cut away the original machine basted seam and the zipper should peek out from under the lapped edge of fabric.
If this is your first lapped zipper I suggest you practice on spare fabric first. That's the great thing about sewing- ALL the stitches can always be removed and you get a second chance ( and third chance and fourth chance and fifth...)