  We study heat flux avalanches occurring at the first order transition in
La(Fe-Mn-Si)$_{13}$-H$_{1.65}$ magnetocaloric material. As the transition is
associated to the phase boundaries motion that gives rise to the latent heat,
we develop a non equilibrium thermodynamic model. By comparing the model with
experimental calorimetry data available for Mn=0.18, we find the values of the
intrinsic kinetic parameter $R_L$, expressing the damping for the moving
boundary interface, at different magnetic fields. We conclude that by
increasing field, thus approaching the critical point, the avalanches increase
in number and their kinetics is slowed down.
