  This is the third paper in a series in which we attempt to put constraints on
the flattening of dark halos in disk galaxies. For this purpose we need to
analyse the observed XV diagrams in edge-on galaxies to accurately measure the
radial HI surface density, the rotation curve and the HI velocity dispersion.
We present the results of the modelling of HI observations of 8 HI-rich,
late-type, edge-on galaxies. In all of these we find differential rotation.
Most systems display HI velocity dispersions of 6.5 to 7.5 km s$^{-1}$ and all
except one show radial structure. There is an increase in the mean HI velocity
dispersion with maximum rotation velocity, at least up to 120 km s$^{-1}$. Next
we analyse the observations to derive the radial variation of the thickness
(flaring) of the HI layer. We find that with the exception of the asymmetric
IC5052, all of the galaxies in our sample are good candidates for 3D mass
modelling to measure the dark halo shape. The flaring profiles are symmetric
and have a common shape, increasing linearly inside the stellar disks and
exponential outside where the gravitational potential is dominated by the dark
halo. In the best example, UGC7321, we find in the inner regions small
deviations from the midplane and accompanying increases in thickness of the HI
layer that are possibly a result of perturbations by a relatively strong bar.
