Being as I own both of these players, I would suggest that you bench Rice for Week 1. Ingram is the more "lucrative" choice between the two, so I would pick him without looking back twice. I've also had better luck using a RB as a flex than most WR's out there on my team.
10 team H2H league, standard scoring [NFL.com]
QB: A. Rogers
RB: MJD, S. Jax, J. Starks, D. Murray, M. Bush
WR: M. Wallace, B. Marshall, P. Harvin, M. Colston, L. Robinson
TE: O. Daniels, J. Gresham
K: Sebastian Janikowski