The classic (and fastest) route is Amphitheater - Saddlerock - Greenman (ASG) from the Gregory Canyon parking lot and ending at the base or top of the summit block. It's about 2.2 miles with 2200' of elevation gain. These trails are clearly shown on this map, where the Gregory Canyon TH is located at the apparent intersection of the Baseline and Flagstaff trails, at the base of Flagstaff Road. George Zack has collected a list of fast times. The trail has changed significantly since the September 2013 flood, including some short re-routes and the addition of a ladder in a badly washed out spot. This route has a Strava segment, but note that Strava can be off by numerous seconds, so it's best to record your actual time in addition to posting your Strava track.
In the old days the standard start was Chautauqua Auditorium, which adds roughly 0.5 mile (relatively flat). Bill Briggs reports that his brother, Roger, ran to the summit of Green from the Auditorium in 35m40s in 1984. Recently, we learned of another fast ascent via a non-standard route by Eric Doub on 5/10/1980 (when Doub was 16?): "I ran Green many times in the 1970s and 80s via this route, and I believe my PR [33m20s] was in spring 1980: W side of Baseline at 6th St. - trail past Amphitheater and Saddle Rock - north ridge direct (later became Habitat Conservation Area, I think) back onto Greenman. On the "north ridge direct" portion, the route involved 3rd class scrambling up and over and down to the Greenman Trail. This route became off limits [requires an off-trail permit for the Habitat Conservation Area] in later years. I think it saved a few minutes."
Zack also reports times for other routes as per these links:
georgezack.blogspot.com/2007/01/fkts-green-mountain-boulder-bear-canyon.html (note that the Bear Canyon and Green-Bear trails have been majorly rerouted and are now MUCH longer than in 2011)
Cordis Hall also reported some "obscure" Green Mtn FKTs:
Notes on some of the more 'obscure' Green times...
Timothy Olson ran 10x Green in 13:45 https://www.strava.com/activities/2394615334/overview
Jackson Brill ran my downhill time at 13:25ish, Strava gave him the edge by a couple seconds but by our self timed button presses had me faster. For a self timed effort we agreed on the worst possible outcome, a tie. https://www.strava.com/activities/2139843470/overview
Kyle Richardson ran the double in 1:49:02 but Strava snubbed him on the CR. https://www.strava.com/activities/1425844707/overview
Leonard Strnad pushed a project to N=4 for N laps of Green in N hours.https://www.strava.com/activities/2120156809/overview
Ordinarily, the Green Mountain EMG-SR-Amp downhill is very technical and rocky in the dry. But owing to its SE aspect and frequent traffic, it's fastest when snow conditions shape up for a rare, buttery smooth singletrack from summit to trailhead. This February, the stars aligned with an exceptional cycle of good snow on Green. A fervor spread in the community. At cold trailheads and in dark winter pubs, runners discussed their favorite lines, what microspikes are best (if any), and what day would be best to go for a PR. Some downhill enthusiasts took it upon themselves to go out specifically to groom the downhill after each new snow, making sure drifts were stomped down and all preferable micro variations were packed down and ready.
This lead to a flurry of speedy downhills over the course of the month, with at least 10 sub-15 minute downhills being recorded on Strava. As of today, 13 of the top 25 all time descents on Strava were run in February, 2022.
In the midst of this fervor, we saw the mens FKT lowered 3 times:
On 2/7 Kyle Moss improved the 4-year-old FKT by a few seconds to 13:23.
Only a week later, conditions were even better, and Kyle Moss broke 13 minutes, descending from the summit disk to the asphalt parking lot in 12:47.
Two weeks later, snow conditions remained extremely tacky and well groomed, allowing Kyle Richardson to take the throne with a 12:40 descent.
After that, the ephemeral snow conditions turned to slush and spring sun, and with it, the Green '22 downhill season faded in local lore.