We infer the intrinsic ionized gas kinematics for 383 star-forming galaxies across a range of integrated star formation rates (SFR{in}[10^-3^, 10^2^]M_{sun}_/yr) at z~<0.1 using a consistent 3D forward-modelling technique. The total sample is a combination of galaxies from the Sydney-AAO Multiobject Integral field Spectrograph (SAMI) Galaxy survey and DYnamics of Newly Assembled Massive Objects survey. For typical low-z galaxies taken from the SAMI Galaxy Survey, we find the vertical velocity dispersion ({sigma}_v,z_) to be positively correlated with measures of SFR, stellar mass, HI gas mass, and rotational velocity. The greatest correlation is with SFR surface density ({Sigma}_SFR_). Using the total sample, we find {sigma}_v,z_ increases slowly as a function of integrated SFR in the range SFR{in}[10^-3^, 1] M_{sun}_/yr from 17+/-3 to 24+/-5km/s followed by a steeper increase up to {sigma}_v,z_~80km/s for SFR>~1M_{sun}_/yr. This is consistent with recent theoretical models that suggest a {sigma}_v,z_ floor driven by star formation feedback processes with an upturn in {sigma}_v,z_ at higher SFR driven by gravitational transport of gas through the disc.