The minimum flow for any run is always a relative term. It depends on your affinity for scraping or dragging and still having a good time with it. I did the jarbidge and bruneau about 3 years ago. We took 6 days for the whole section, and launched at about 1400 cfs, but it was dropping the whole time, and by the last day on the bruneau, we were down to about 700. The boatmen I had on the trip were pretty skilled at running technical stuff, and had a good time , but that being said, they were not happy with that low a flow on the bruneau. Don't even think about launching the jarbidge with rafts at 650 cfs, if ever. One of the rafts also ripped a big hole in the floor on a sharp rock somewhere in the class II boogie water on the last day of the bruneau, so if you love your boat, don't take it.
I would say at those flows, a more enjoyable plan is a self supported kayak or ducky trip. You could also take a shredder or small cat (10' or so) and have a good time with it. It is still quite fun in a kayak at those levels, and the scenery fantastic. I second the watch for rattle snakes remark.