So, it seems you can't fix this just by running chlorine or whatever down the drain and hoping.

Turns out the reason your kitchen sink stinks is because you have years worth of grease, hair and other shit stuck in your drain.

Time to take it apart and clean it.... 

Process

1. Disassemble your drain basket strainer from your sink and remove.
2. Remove the thick buildup
   Scrape it into the garbage using paper towel or a plastic scraper. Don’t push it down the drain.
3. Soak the parts
   Put them in a bucket with very hot water and a generous amount of dish soap for 20–30 minutes.
4. Scrub thoroughly
   Use a bottle brush or old toothbrush, especially inside the brass tube, around threads, beneath the strainer flange, and in any grooves.
5. Reassemble with new seals
   Replace dirty, hardened, or distorted rubber and slip-joint washers. 

After reassembly, fill the sink halfway, release it, and check underneath with dry paper towel for leaks.

References