Bleach will get some of it out if you pour a gallon down the drain and let it set for a few minutes. Another product is called thrift and you can get it from the plumber store, you mix it up and pour it in according to directions. It works great!
I have recently just done mine. They have been partially blocked for years. I tried drano which did not work. I spent hours boiling water and putting it down the drain. Once it got through the blockage, I put the hot water on the hotest temp and left it run for a hour. Most sink blockages are greases which will desolve with all the hot water.