Obtain a vinyl sheet that is the same color as the slats in the chain link fence. Vinyl sheets are available from home improvement stores.
Extract a vinyl slat from the chain link fence. Ensure that it is in ideal condition, because you will use it as a template for the replacement slats.
Place the vinyl sheet on a flat surface. Lay the slat on the vinyl sheet.
Trace around the edges of the vinyl slat with a pencil. Cut along the lines with a utility knife to produce a new slat.
Sand the edges of the new slat to remove the burr and make them smooth. You can complete the task in a short amount of time if you use an electric sander, but sandpaper is also effective. Begin with a rough grade of sandpaper, such as 100-grit, and change to progressively finer grades until the edges are as smooth as you wish. Wipe the dust off the slats with cloth.
Repeat Steps 3 and 4 for the number of slats you need to replace.
Weave the new slats through the holes in the chain link fence, in the same direction as the original slats. Replace the slat you used as a template.