I walked it once about 20 years ago, starting at Jenolan. First day there was a father and son who were running the track in a day, had left from the Katoomba end that morning.
My partner and I have done it there and back in a day. Quite a painful experience. Forgetting Peter Treseder's unsubstantiated claim, the best runners do it in around 3.5 hrs. I was around 5.5 hrs. If the plan is to walk only then you will most likely need a headlamp. Some sections you will be able to manage 4 or 5 k/h pretty easy but the hills will slow your average down. It is a good track to do by headlamp and you be amazed by how fast wombats can run when spooked.
If you are fit, used to doing long days and have a good pace on smooth tracks, it is a fairly easy walk to do in a day. It is not hard to average 5kph so you can do it in about 9 hours of walking time. Could do it all in daylight if you get an early start. I prefer starting at Katoomba, but go with whatever makes the logistics easier. Could be easier to get dropped off at Jenolan and then walk back to your car at Katoomba.
Pick a full moon in spring or Autumn. Turfa is right, a longish day but doable during daylight as long as all goes well and you start at first light but I would struggle maintaining a 5kph average over the entire track just walking. Breaks for food and photos or just rest will effect your average speed considerably. Either direction is pretty much the same and just work that out based on your own logistics.
K to J is an annual one-day race. Be there on the wrong day and the thundering herds will run you off the track! (Not true, they generally say 'excuse me'.) We have had to guide a few runners back onto the track when they got down onto the river too soon. Cost them time.
Coxs R is really a late morning tea, or an early lunch. Better by far to go to the next river, at the foot of the Black Range, or even to the campsite beside the Jenolan road (tank water). Mind you, if everyone carried a couple of Ls of water, you could camp anywhere along the B Range.