You might want to try in the cleaning forum. If it's tarnish, then a mild metal polish might clean it up. If it's red/brown RUST, then you've probably already had the plating destroyed and the base steel is rusting now.

I suspect that rust on the steel is coming through and destroying the plating. If this is a valuable lamp, you could get it re-plated.

I had one that received shipping damage to the finish, bought it for fraction of original cost. At beauty supply, found nail polish that matched well and touched up the damaged finish. Not noticeable at all, installed in my house.