People differ on whether lane splitting on motorcycles should be legal or not, but this technique — as with, for example, permitting “right turns on red” at traffic lights — has more to do with the convenience of drivers or riders than it does with best safety standards. In any event, whatever your stance on the subject, it is NOT legal in Washington State.

The WA law specifically states that no person shall operate a motorcycle between lanes of traffic or between adjacent lines or rows of vehicles; nor can a motorcycle overtake and pass in the same lane occupied by the vehicle being overtaken.
You can read more about the legal situation regarding lane-splitting in Washington State, on the WSP Inside-Out blog.