I had a problem with my kitchen sink drain too. I didnt biuld the house, had no knowledge of what route the drain line took. I tried clearing it out with 25ft long drain cleaner, that got me no-where. Called a plumber, he ran his drain cleaner down it, put more than 40ft down that drain. That got it working again, but not perfect. Slow flow, shall we say. Later tore up the tile floor, pulled up the cement board for a new tile floor, removed all the kitchen cabinets. removed some of the sub floor to re-position the hot and cold water lines for the sink so they came out the wall instead of coming out the floor. Did the same with the drain line. Discovered the the drain line runs near horizontal the entire length of the house. The only fall is the height of the floor joists, less than 10" total. I changed the sharp 90 degree elbows for long radius elbows and eliminated about 6 feet of extra pipe that they had in the wall. The pipe in the wall had an accumulation of fat in it with a hole going through the blockage the diameter of the stem of the drain cleaner or about 3/8". The rest was a solid plug. I think I have it sorted now and it should be a lot easier fishing something through it....
