  In this note, we prove a $L^p$ version of the well known stability estimate
for regular Lagrangian flows derived by Gianluca Crippa and Camillo De Lellis
in \cite{crippa2008estimates}. As far as we know, the only estimate of this
kind readily available in the literature is for the case $p=1$. With minor
modifications to the proof in \cite{crippa2008estimates}, we show that an
analogous estimate holds in $L^p$ norm with $p \in (1, + \infty)$.
