Boron arsenide (BAs) has ultra-high thermal conductivity (κ) and exceptional semiconductor properties, positioning it a prime candidate for heat control and management systems in electronic devices. Investigating the κ and phonon transport properties of BAs films across multiple scales is essential for the design of micro-nano integrated devices. Utilizing the machine learning (ML)-driven moment tensor potential (MTP), this work systematically studies the effects of various parameters including thickness, temperature and isotope on the cross-plane (CP) and in-plane (IP) anisotropic κ of BAs films. This study reveals that boundary scattering resulting from the reduction in thickness significantly diminishes κ, with this size effect becoming more pronounced at lower temperatures. Furthermore, the CP direction experiences a stronger size effect on phonon heat transport than in the IP direction, attributed to the shorter phonons mean free path (MFP). The isotope effect and size effect mutually inhibit each other, which relates to the scattering mechanisms that restrict phonon heat transport. The contribution of acoustic phonon branches to the CP and IP κ align with variations in total κ relative to temperature and thickness. Notably, the κ of the longitudinal acoustic (LA) branch decreases more than that of the transverse acoustic (TA) branch as film thickness decreases, mirroring the same stronger size effect observed in the CP direction.