I don't think that anyone would specialize in this type of duck. As you can see from the regulations you would only be allowed 4 King Eiders as a non-resident. You probably have to hunt along the Bering Coast between the nesting grounds, Barrow, and the wintering, Aleutians. There are some duck hunting guides out there but the King Eiders would seem to be an incidental kill.
"SEA DUCKS (harlequin ducks, long-tailed ducks (formerly oldsquaw), all eiders, scoters and mergansers): Resident hunters may not take more than 6 daily, 12 in possession each of harlequin or long-tailed ducks. Daily sea duck limits for nonresidents are equal to general duck limits for the zone (7, 8 or 10). Nonresidents may not take or possess more than 20 sea ducks per season, including no more than 4 each of harlequin, long-tailed duck, black scoter, surf scoter, white-winged scoter, common eider, or king eider per season. Steller's and spectacled eiders are closed statewide."