If you want a scenic route up Kings Peak, but without the crowds, this is the route for you. Traversing the bench between Milk Lake and Anderson Pass isn't difficult and there are almost no crowds. It is slightly longer than the Henrys Fork Route though. Four days round trip is recommended, though a strong hiker could certainly do it in less.
First, drive to the town of Duchene, which is along US Highway 40. From Duchene, turn north onto State Highway 87. Follow State Highway 87 until it joins with State Highway 134 (this is where state Highway 87 heads due east instead of continuing north) between milepost 15 and 16. Follow State Highway 134 north to the little town of Mountain Home. Where State Highway 134 begins to head due east at Mountain Home, Continue north on the Moon Lake Road. After five miles, turn east on the Yellowstone River Road and to the Yellowstone River Power Plant. Continue along the Yellowstone River road to the trailhead at the end of the road, passing the Yellowstone River Dude Ranch and two campgrounds along the way.
From the Swift Creek Trailhead, I would highly recommend that you not take the trail directly up Yellowstone Creek. The trail isn’t bad, but there are no views for many miles and at least a day or two. The trail is in a tunnel of timber the whole way and is more like hiking in the North Woods of Minnesota than the Rockies. The best way to climb kings from the Swift Creek Trailhead, is to take the Swift Creek Trail to Farmers Lake and then Bluebell Pass, and then descend to Milk Lake.
From the trailhead (8000 feet elevation) at the Swift Creek Campground, follow the trail north. After just a short distance, you will reach a junction. Take a right here on the Swift Creek Trail. The trail switchbacks onto a ridge high above and to the west of Swift Creek so make sure to take plenty of water. After following the ridge for a few miles, the trail levels out and eventually reaches Swift Creek. The trail continues to follow Swift Creek, passing many beaver dams and ponds, crossing it twice on bridges before reaching Deer Lake, which is at 10,200 feet and 6 miles from the trailhead.
After Deer Lake, continue on the trail and after 0.75 miles, you will come to a junction. Turn left and follow the trail past Farmers Lake and over Bluebell Pass, and then descend to Milk Lake. From Milk Lake, follow the base of the ridge to the east all the way to Anderson Pass. The route passes through many spectacular and beautiful alpine meadows full of wildflowers. There is no trail after Milk Lake, but the cross-country route is easy to find since there are open views and travel is not difficult.
From Milk Lake, just continue contouring along the long and scenic bench, staying west of the Kings Emmons Ridge, South Kings Peak, and Kings Peak. Along the way there are only a few obstacles such as a short section of logs and some rocks.
One near Anderson Pass, climb up to the pass (there is a trail to the pass that you will meet). If you head west a bit, it will be easier. From Anderson Pass, follow the ridge south over King Peak. The route is about 40 miles round trip, and usually takes four days.
A good pair of boots is needed.