To restore shine to a dull kitchen sink, I recommend Autosol 75ml Chrome And Metal Polish or 3M 200g Stainless Steel Cleaner And Polish.
I have used both products at Bunnings stores to polish our rangehoods and ovens to great effect.
It is difficult to estimate how long the polish will last in a kitchen sink. I would expect buildup on the sink is caused by food and soap residue. I've noticed that when you let Autosol to sit on the surface for a while, it actually loosens up surface stains.
I recommend trying Autosol first and if you are not satisfied with its performance, you can then try 3M Polish.
Please make sure to wear personal protection such as gloves and goggles. Make sure to follow the safety instructions printed on the packaging. - EricL
