You know, as long as you could make a mechanical device that will assure less than five rounds per second can be fired, it would not be considered a machine gun according to Washington law. I'll have to check out the federal law but if the federal still classifies it as one you'd just need to do the ATF paperwork and get the tax stamp and it would be legal here.
So according to Washington law, a three round burst would be ok to own if that is indeed the case.
(11) "machine gun" means any firearm known as a machine gun, mechanical rifle, submachine gun, or any other mechanism or instrument not requiring that the trigger be pressed for each shot and having a reservoir clip, disc, drum, belt, or other separable mechanical device for storing, carrying, or supplying ammunition which can be loaded into the firearm, mechanism, or instrument, and fired therefrom at the rate of five or more shots per second.
ETA
Looks like the fed is more strict in their definition but I think we should be able to lawfully own a three round burst AR with the proper federal paperwork.
Any weapon which shoots, is designed to shoot, or can be readily restored to shoot, automatically more than one shot without manual reloading, by a single function of the trigger