Mix together 1 cup white distilled vinegar and 1 tsp. plain table salt. Add all-purpose flour to the mix, a tablespoon at a time, stirring thoroughly after each addition. Stop adding flour when the mixture forms a paste.
Apply the paste to the solid brass with a soft rag. Wait 15 to 20 minutes.
Rinse the brass well with plain water. Buff the brass with a buffing pad until the scratches are completely gone and the surface is dry.
Put on a pair of rubber gloves. Take your brass outdoors or to another very well-ventilated area.
Dampen a soft rag with plain household ammonia.
Buff the scratches out of the brass gently. Rinse the brass piece thoroughly and let it air-dry. It may be necessary to re-lacquer the brass once it is dry.