Angle and temperature dependent torque magnetization measurements are reported for the organic superconductor kappa-(BEDT-TTF)2Cu(NCS)2, at extremely low temperatures (approx. Tc/10^3). Magneto-thermal instabilities are observed in the form of abrupt magnetization (flux) jumps. We carry out an analysis of the temperature and field orientation dependence of these flux jumps based on accepted models for layered type-II superconductors. Using a simple Bean model, we also find a critical current density of 4x10^8 A/m^2 from the remnant magnetization, in agreement with previous measurements.