Washington is a great place to be! If you start a digital nomad trip from there, your state taxes will be as simple as possible.

Regarding being dual-taxed, the US has dual taxation treaties with almost every country, so you can deduct the taxes you pay to another country from your US taxes. e.g. If you move to France, you'll pay taxes there, and when you file in the US you'll get credit for those taxes paid. There are numerous other complications for federal taxes as well! But you probably won't flat-out pay double.