  This article deals with the error estimates for numerical approximations of
the entropy solutions of coupled systems of nonlocal hyperbolic conservation
laws. The systems can be strongly coupled through the nonlocal coefficient
present in the convection term. A fairly general class of fluxes is being
considered, where the local part of the flux can be discontinuous at infinitely
many points, with possible accumulation points. The aims of the paper are
threefold: 1. Establishing existence of entropy solutions with rough local flux
for such systems, by deriving a uniform BV bound on the numerical
approximations; 2. Deriving a general Kuznetsov-type lemma (and hence
uniqueness) for such systems with both smooth and rough local fluxes; 3.
Proving the convergence rate of the finite volume approximations to the entropy
solutions of the system as $1/2$ and $1/3$, with homogeneous (in any dimension)
and rough local parts (in one dimension), respectively. Numerical experiments
are included to illustrate the convergence rates.
