As promised, here's the info for applying via Speaker Frank Chopp (one of the three people to select the Charter Commission).
It's basically the same as the Lt. Governor's office - write/e-mail them to self-nominate or to nominate someone. If you are self-nominating, give full details about your background (both personal and professional that might be pertinent) as well as your resume. If you are nominating someone else, maybe be sure that they want to be nominated so that they can send in their resume if asked for one.
339C Legislative Building
PO Box 40600
Olympia, WA 98504-0600