Are localized rings always flat as $R$-modules? We know this is true for commutative ring, but if $S\subset R$ is a left and right Ore set, and $S^{-1}R$ its localization by this Ore set, is this always a flat $R$-module?

This is Proposition 2.1.16 in McConnel+Robson's book on _Noncommutative Noetherian Rings_.