  The kinetic Sunyaev-Zel'dovich (kSZ) effect is a secondary cosmic microwave
background (CMB) anisotropy induced by the scattering of CMB photons off
intervening electrons. Through cross-correlations with tracers of large-scale
structure, the kSZ effect can be used to reconstruct the 3-dimensional
radial-velocity field, a technique known as kSZ tomography. We explore the
cross-correlation between the CMB and line-intensity fluctuations to retrieve
the late-time kSZ signal across a wide redshift range. We focus on the CII
emission line, and predict the signal-to-noise ratio of the kSZ tomography
signal between redshifts $z=1-5$ for upcoming experiments. We show that while
instruments currently under construction may reach a low-significance detection
of kSZ tomography, next-generation experiments will achieve greater
sensitivity, with a detection significance of $\mathcal{O}(10^2-10^3)$. Due to
sample-variance cancellation, the cross-correlation between the reconstructed
velocity field from kSZ tomography and intensity fluctuations can improve
measurements of %the scale-dependent bias contributions from new physics to the
power spectrum at large scales. To illustrate this improvement, we consider
models of the early Universe that induce primordial local-type non-gaussianity
and correlated compensated isocurvature perturbations. We show that with CMB-S4
and an AtLAST-like survey, the uncertainty on $f_{\rm NL}$ and $A_{\rm CIP}$
can be reduced by a factor of $\sim 3$, achieving $\sigma(f_{\rm NL}) \lesssim
1$. We further show that probing both low and high redshifts is crucial to
break the degeneracy between the two parameters.
