Peel all the Silly String off the leather jacket, using your fingers, and discard it.
Lay the jacket flat, with the area the Silly String was removed from facing up.
Mix equal parts white vinegar and water in a spray bottle, and spray the affected area. Let it set for a few minutes, and then use a damp rag to soak up the vinegar mix.
Apply a dab of leather stain remover evenly over the area, using a clean rag. Let it set for a few hours, and then wipe it off with a dry rag.
Bring the jacket to a professional cleaner, if the stain remains.