Using a garment with a good pocket size and shape, make a pattern template out of paper. My linen was a bit small, so I added a flannel strip on the top. It works well as a decorative element too. Press the linen and the flannel and place right sides together. If you like, you can use interfacing behind the stitching.
Pin the paper pattern so that the stitching comes out straight and centered. Leaving a 2" gap on one of the long sides, stitch the rest of the way around at the outline of the paper.
Trim the excess fabric and turn this assembly inside out, so the right sides are now out. Fold the sides of the opening so they match up. Use a chopstick or something blunt but pokey to crispen up the corners. Hand whip stitch the opening so that it now resembles a pillow with no stuffing. At this point (pocket is not attached yet), Sew a row of stitching evenly around the perimeter. This helps to stabilize the raw edges inside the pillow pocket. I used one of the decorative stitching patterns my sewing machine has built in.
Put the garment on, to decide where the best pocket placement is and pin the pocket in that place. Using a double length of sewing thread the same color as the linen (and beeswaxed) hand whip stitch the pocket sides and bottoms to the lining of the coat.