Kernel methods are of current interest in quantum machine learning due to similarities with quantum computing in how they process information in high-dimensional feature (Hilbert) spaces~\cite{Schuld2021}. Kernels are believed to offer particular advantages when they are hard to simulate classically, so a kernel with the right kind of complexity, or nonclassicality, is considered important. While these points have been extensively researched for discrete states such as qubits, relatively few works have considered them in the continuous variable regime. Kerr nonlinearities, already a known route to universal continuous variable (CV) quantum computation, are also a strong source of nonclassicality for machine learning.