This is the third paper in a series in which we attempt to put constraints on the flattening of dark halos in disk galaxies. We observed for this purpose the Hi in edge-on galaxies, where it is in principle possible to measure the force field in the halo vertically and radially from gas layer flaring and rotation curve decomposition respectively. For this purpose we need to analyse the observed XV diagrams in such a way as to accurately measure all three functions that describe the planar kinematics and distribution of a galaxy: the radial Hi surface density, the rotation curve and the Hi velocity dispersion. In this paper, we first present the results of the modelling of our Hi observations of 8 Hi rich, late-type, edge-on galaxies. We find that 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 in this property. 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 Hi observations to derive the radial variation of the thickness of the Hi layer. The combination of these gas flaring measurements with the Hi kinematics measurements allow us to measure the total vertical force of each galaxy assuming hydrostatic equilibrium. 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 with respect to the galactic centres 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 of the gravitational field by a relatively strong bar.