To make your own jacket or coat sleeve lining, start with smooth, silky fabric, and avoid using coarse, textured fabrics that cause static cling when you pull your outerwear on and off. Smooth fabrics make better sleeve lining than textured fabrics because they are soft and do not create static. Also, if your outerwear has an elasticated or pleated cuff, use a seam ripper to open the cuff, or elastic casing, before making the lining.
Turn the jacket or coat inside out.
Wrap the lining fabric right side out around the sleeve, with the lining fabric's raw edges coming together on top of the underarm seam.
Pin the lining to the sleeve right on top of the sleeve's underarm seam.
Smooth out any remaining wrinkles in the lining fabric, then pin the lining fabric to the sleeve's shoulder seam and cuff.
Cut the lining fabric 1/2 inch beyond the sleeve's seam lines. Remove the pins.
Set the sewing machine to make a finishing stitch, then sew all the way around the piece of lining material.
Fold the sleeve lining in half the long way, with the right sides together, so the long straight underarm edges are lined up.
Set the sewing machine to make a short, straight stitch and sew the straight underarm seam.
Turn the lining right side out and slide it over the still-inside-out jacket sleeve. Line up the shoulder curves and underarm seams.
Fold the lining's shoulder edge under 1/2 inch and pin the lining to the jacket's shoulder seam.
Hand sew the folded edge to the jacket, making a backstitched seam. Remove the pins.
Fold the sleeve's cuff edge around the lining and hand sew the lining to the cuff edge, making a blind hem stitch.
If you removed an elastic casing or pleated cuff before you started to make the lining, fold everything on the sleeve's cuff back into its original position. Use the sewing machine's straight stitch to sew it back, following the original stitching line.