Measurements of the growth rate of structures at \(z < 0.1\) with peculiar velocity surveys have the potential of testing the validity of general relativity on cosmic scales. In this work, we present growth-rate measurements from realistic simulated sets of type-Ia supernovae (SNe Ia) from the Zwicky Transient Facility (ZTF). We describe our simulation methodology, the light-curve fitting and peculiar velocity estimation. Using the maximum likelihood method, we derive constraints on \(f\sigma_8\) using only ZTF SN Ia peculiar velocities. We carefully tested the method and we quantified biases due to selection effects (photometric detection, spectroscopic follow-up for typing) on several independent realizations. We simulated the equivalent of 6 years of ZTF data, and considering an unbiased spectroscopically typed sample at \(z < 0.06\), we obtained unbiased estimates of \(f\sigma_8\) with an average uncertainty of 19% precision. We also investigated the information gain in applying bias correction methods. Our results validate our framework which can be used on real ZTF data.