Using the atomic cluster expansion (ACE) framework, we develop a machine learning interatomic potential for fast and accurately modelling the phonon transport properties of wurtzite aluminum nitride. The predictive power of the ACE potential against density functional theory (DFT) is demonstrated across a broad range of properties of w-AlN, including ground-state lattice parameters, specific heat capacity, coefficients of thermal expansion, bulk modulus, and harmonic phonon dispersions. Validation of lattice thermal conductivity is further carried out by comparing the ACE-predicted values to the DFT calculations and experiments, exhibiting the overall capability of our ACE potential in sufficiently describing anharmonic phonon interactions. As a practical application, we perform a lattice dynamics analysis using the potential to unravel the effects of biaxial strains on thermal conductivity and phonon properties of w-AlN, which is identified as a significant tuning factor for near-junction thermal design of w-AlN-based electronics.