  Cosmological constraints from key probes of the Euclid imaging survey rely
critically on the accurate determination of the true redshift distributions,
$n(z)$, of tomographic redshift bins. We determine whether the mean redshift,
$<z>$, of ten Euclid tomographic redshift bins can be calibrated to the Euclid
target uncertainties of $\sigma(<z>)<0.002\,(1+z)$ via cross-correlation, with
spectroscopic samples akin to those from the Baryon Oscillation Spectroscopic
Survey (BOSS), Dark Energy Spectroscopic Instrument (DESI), and Euclid's NISP
spectroscopic survey. We construct mock Euclid and spectroscopic galaxy samples
from the Flagship simulation and measure small-scale clustering redshifts up to
redshift $z<1.8$ with an algorithm that performs well on current galaxy survey
data. The clustering measurements are then fitted to two $n(z)$ models: one is
the true $n(z)$ with a free mean; the other a Gaussian Process modified to be
restricted to non-negative values. We show that $<z>$ is measured in each
tomographic redshift bin to an accuracy of order 0.01 or better. By measuring
the clustering redshifts on subsets of the full Flagship area, we construct
scaling relations that allow us to extrapolate the method performance to larger
sky areas than are currently available in the mock. For the full expected
Euclid, BOSS, and DESI overlap region of approximately 6000 deg$^{2}$, the
uncertainties attainable by clustering redshifts exceeds the Euclid requirement
by at least a factor of three for both $n(z)$ models considered, although
systematic biases limit the accuracy. Clustering redshifts are an extremely
effective method for redshift calibration for Euclid if the sources of
systematic biases can be determined and removed, or calibrated-out with
sufficiently realistic simulations. We outline possible future work, in
particular an extension to higher redshifts with quasar reference samples.
