We characterize single-mode vacuum squeezing generated by a SNAIL Parametric Amplifier (SPA) operated under conditions representative of practical sensing and qubit-readout experiments. Motivated by prior expectations that Kerr-induced distortion limits squeezing in degenerate parametric amplifiers, we studied squeezing as a function of external flux and pump power to explore operating points where Kerr nonlinearity is theoretically minimized. We find that for squeezing operation at a fixed frequency, Kerr varied by about a factor of two and the achievable squeezing showed no significant dependence on Kerr. Rather than Kerr, the squeezing is dominated by internal resonator loss and insertion loss in the microwave chain as confirmed by theoretical modeling. These results indicate that, in practical SPAs, reducing loss, rather than suppressing Kerr, is the primary route to improved squeezing performance.