You may not need to do anything special with your stitches after chin implant surgery. If your surgeon needs you to clean the area they will tell you.
Stitches inside the mouth are usually kept clean with mouthwash and water until they dissolve.
You may have paper tapes or steristrips over the stitches, do not remove these tapes. They are an important part of the repair. You may get them wet but do not rub soap into them. Many doctors use stitches that dissolve. This mean your stitches do not have to be removed.