I have a black and decker digital iron also(don't know model #). I don't know what is on your sole plate but I've used a Mr. Clean magic eraser on mine(when cold of course) and it worked well. Maybe worth a try.
Or another method I use on a shiny metal surface like that is DRY baking soda. Rub well with a paper towel or rag(some stains do take some elbow grease)and stains should come off. I then vacuum up the dry baking soda and then rub item with a damp cloth to finish off. Have used this regularly on the chrome on my toaster for years with great success.