I did this after riding my bike 430 miles in three days from my home in Boulder, CO to the Henry's Fork Trailhead. Quick report from Strava:
"I accidentally started from the horse trailhead, which was 3min down the road from the hikers trailhead. So, 3:58:37 from car-to-car (i.e., the farthest up that cars are allowed to park).
Didn’t go out particularly hard but sorta just warmed into it to see where my legs were at. Filled water at Elkhorn Creek. Trail finally turned up on the kick to Gunsight and I felt more in my element on the traverse over to the base of Kings itself. Upon actually seeing the mountain in person I could see no reason to go all the way over to Anderson Pass before heading up, so I just cut straight across and started marching up the talus slope to the summit.
Spent about 90sec on top taking photos then headed back down the way I came. Really nothing to report. Tried to keep running hard the last hour as the trail flattened back out, the heat cranked up, and the smoke rolled in. Glad I did, to get that sub-4hr. Refilled my flask at Elkhorn Creek on the way back. I was dry!
Had a loooong creek soak afterwards, my first bathing of the trip. Then filtered and drank a gallon of water, ate some food, filtered three more liters for the bike, and pedaled off into one of the more heinous bits of riding I’ve had in a long time.
Elkhorn Creek - 48:30
Gunsight Pass - 1:36:45
Foot of Talus - 1:57
Summit - 2:16:50
Left summit - 2:18:20
Foot of Talus - 2:30
Gunsight - 2:45:50
Elkhorn Creek - 3:19:30
Finish - 3:58:37"
Jason Dorais held the overall time before this of 4:13:31 (summit in 2:18) on July 24th, 2015 as documented here: https://www.strava.com/activities/353238091/overview
Travis Morrison had a very fast trailhead-to-summit time of 2:17:36 on July 14th, 2018 as documented here: https://www.strava.com/activities/1705295882/overview
I only bested Travis' ascent time because of the more direct route I took from Gunsight Pass to the summit of Kings. Obviously, my downhill was a lot faster than both of theirs---I submit that this was because I was running the mountain on very tired legs (because of all the biking in the previous days), so I didn't have fresh legs for the uphill but I was sufficiently warmed up for the downhill.
Either way, this can go much MUCH faster (3:30?) if anyone cares to give it a rested, focused go using my more direct route from Gunsight to the Summit and back. Have at it!