...the Gibbs Free Energy, incorporating both enthalpies and entropies, together with temperature, to find out the temperature at which the reaction becomes spontaneous (ie no activation energy/autoignition etc).

A negative Gibbs free energy tells you the reaction is spontaneous with regards to the energy/ entropy of the initial and final molecules (thermodynamics) but this doesn't mean it has no activation energy (kinetics). Generally, in all chemical reaction cases there will be a positive activation energy. An intermediate transition state which is of higher energy than the final and initial states commonly exists. Where you may be going wrong is that there exists an alternative Arrhenius equation relating the Gibbs free energy change associated with the transition state to the activation energy.

But this stresses an important point of the original question, which you do address. The kinetics of the process are of paramount importance when deciding if a substance is flammable at given conditions not just the thermodynamics e.g. flour is found to be flammable when finely dispersed as a particulate aerosol.

Examples of processes without activation energies are nuclear reactions, I believe.