  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.
