<p>In this article, we study the existence of insensitizing controls for a nonlinear reaction-diffusion equation with dynamic boundary conditions. The problem consists in finding a control for a system with partially unknown initial data, such that a specific functional is insensitive to small perturbations of this data. More precisely, the functional considered here depends on the norm of the state in a subset of the bulk together with the norm of the tangential gradient of the state on the boundary. This problem is equivalent to a (relaxed) null controllability problem for an optimality system of cascade type, with a zeroth-order coupling term in the bulk and a second-order coupling term on the boundary. To achieve this result, we linearize the system around the origin and analyze it by the duality approach and we prove a new Carleman estimate for the corresponding adjoint system. Then, a local null controllability result for the nonlinear system is proven using an inverse function theorem.</p>