good god, i just got done doing this. I must have tried every product available. Mine was a kitchen sink also.
First wave of attack: Use Drano max. Dont use the generic brand, dont use competing brands. Drano max is seriously the sh*t. If the water isnt going down AT ALL, use the whole bottle. If its just slow, use 1/2 of it.
Second Wave of attack: Liquid plumer crystal foaming pipe cleaner. You pour about a tablespoon of these cyrstals in with cup of water, and this stuff goes to town.
Use em in combination and it works like a charm. I had to repeat the application twice, but it was worth it.