Localization using time-difference of arrival (TDOA) has myriad applications, e.g., in passive surveillance systems and marine mammal research. In this paper, we present a Bayesian estimation method that can localize an unknown number of static sources in 3-D based on TDOA measurements. The proposed localization algorithm based on particle flow (PFL) can overcome the challenges related to the highly nonlinear TDOA measurement model, the data association (DA) uncertainty, and the uncertainty in the number of sources to be localized. Different PFL strategies are compared within a unified belief propagation (BP) framework in a challenging multisensor source localization problem. In particular, we consider PFL-based approximation of beliefs based on one or multiple Gaussian kernels with parameters computed using deterministic and stochastic flow processes. Our numerical results demonstrate that the proposed method can correctly determine the number of sources and provide accurate location estimates. The stochastic flow demonstrates greater accuracy compared to the deterministic flow when using the same number of particles.