Not a kayaker, so I can't answer that part.
In a ducky or Pack Cat, maybe 5-600 cfs, with a wary eye to potential pin/entrapment situations. Very close-set rocks in the whitewater reaches, and the boulders at the base of Narrow Falls might be pretty shallow– worth a scout.
After the peak, when the water's warmer and it's not so gripping to wade, you could run a duck in a few hundred cfs, if you were willing to wade it over bars and maybe portage some boulder jams. At that flow, it's a full day's trip from the Routt put-in to Six Mile Gap. Not much traffic.
For a raft (especially with a load) I wouldn't run lower than 800 cfs (and that takes a lot of oar-work to get through clean. I ran it with a narrow 15 ft. cat and one passenger: fun, but a workout.
541 cfs at the moment.
The Six Mile takeout is a) easy to miss because the channel splits (when you see a freestanding rock tower river left, stay hard left); b) has a steep but maintained trail about 1/4+ mile to the parking lot. It's about 5 ft. wide, so large rafts need to be deflated and rolled. Most people carry the frame and tubes up separately. Solo boating in a large raft might be a bad move.