On Tue, 24 Jun 2014 08:54:24 -0700 (PDT), trader_4
wrote:

If what you're saying is the washer is backing up into
the kitchen sink, then you have an obstruction in the line
further down from both the washer and the kitchen sink.
The washer puts enough volume in there, it can't get
through, so it backs up. That is the most likely source
of the problem.

What happens if you fill the sink with water and let it
all go at once? Drains slower than it should?

I'd be curious if the drain line is pitched enough - towards the
drain?

The GD instructions mention to pitch the P-trap / line...