High-accuracy H I profiles and linewidths are presented for inclined ((b/a)degrees <0.5) spiral galaxies in the southern Zone of Avoidance (ZOA). These galaxies define a sample for use in the determinations of peculiar velocities using the near-infrared Tully Fisher (TF) relation. The sample is based on the 394 H I-selected galaxies from the Parkes H I Zone of Avoidance survey (HIZOA). Follow-up narrow-band Parkes H I observations were obtained in 2010 and 2015 for 290 galaxies, while for the further 104 galaxies, sufficiently high signal-to-noise (S/N) spectra were available from the original HIZOA data. All 394 spectra are reduced and parametrized in the same systematic way. Five different types of linewidth measurements were derived, and a Bayesian mixture model was used to derive conversion equations between these five widths. Of the selected and measure galaxies, 342 have adequate signal to noise (S/N > 5) for use in TF distance estimation. The average value of the S/N ratio of the sample is 14.7. We present the H i parameters for these galaxies. The sample will allow a more accurate determination of the flow field in the southern ZOA which bisects dynamically important large-scale structures such as Puppis, the Great Attractor, and the Local Void.