My hot tip for running the Uncompagre is to continue driving north and go to Escalante instead.
In all seriousness, I have done this run once at about 700 cfs. At that level it felt like fast and pushy 4+ but with some very shallow and sharp rocks all around you. Not that hard, but if you flipped, you would get absolutely destroyed. The lack of boofs, cool moves, etc. combined with the possibility of getting decapitated makes for a pretty low quality run. Plus it is really short.
If you still want to do it after reading this description, I would guess the bare minimum is somewhere around 300cfs, but I wouldn't do that to my kayak.