Flaring is the opposite of tapering; so, instead of the disk tapering off to zero thickness as you move away from the center, it gets thicker instead. Just from common sense reasons, it can't flare very much, if it does. If it does at all, though, their model fails badly. Check Fig. 5 in their paper; if dh/dR is as little as 0.3 (this means that if you go 1 kpc further out, the disk effectively thickens by 300 pc), all of a sudden their results are quite consistent with a lot of dark matter being present. They dismiss the possibility of flaring of the thick disk by saying that if it was all that big, it would have been detected conclusively by now. I don't think that is at all a safe assumption in this case.