Try this: 1 cup of baking soda, 1 cup of table salt, one cup white vinegar.
Into dry sink (make sure there's no water in it), pour baking soda, then salt then vinegar. Wait 10 minutes and flush with boiling water.
If that doesn't work, it's really pretty easy (albeit a little messy) to take apart the little bend in the pipe under the sink, which is where the problematic stuff often collects.
Depending on the age of the plumbing these accumulations can be minor to pretty deep. Once the velocity of the water flow slows (due to deposits) it quickly gets worse. Proper use of the drain will also keep it running free. I would recommend pulling the P trap and snaking the wall penetration. Then reassemble every thing and run about 20 gal of pure hot water through it this will flush and dissolve minor grease deposits that remain. Then about once a month you can simply run the hot water through. I cleared my kitchen drain some 15 years ago and have been using this method every since with no trouble (or chemical additions)