When my washer drains it backs up into the kitchen sink. Obviously there is buildup . ?

Question

what works really well to flush that out?

Answer 1

You can start with pouring boiling water down the drain.

Answer 2

If this is a new problem use a non corrosive pipe cleaner. If it were a p trap it would over flow at the connection. If this has always been a problem, check the length of the stand pipe( the pipe that you are draining into). It should be a min. of 18", another problem could be with your waste vent. If it is not properly vented the drainage causes a kind of vacuum. It needs to pull air. It is kind of like filling a straw with liquid and holding you finger on one end- nothing comes out, when you take your finger off it drains. Waste water drainage works on the same principle.  

Answer 3

You may need to drop the trap under the sink and check to see if there is a blockage, if not the blockage is further down the drain.

I assumed you meant your dishwasher?  If so, you probably have a special pipe under the sink at the trap that allows the dishwasher to drain through the p or s trap.  A blockage there will cause water to fill the sink.  Been there, done that, but we also have a garbage disposal in our kitchen sink.