We consider a simplified model of protein folding, with binary degrees of freedom, whose equilibrium thermodynamics is exactly solvable. Based on this exact solution, the kinetics is studied in the framework of a local equilibrium approach, for which we prove that (i) the free energy decreases with time, (ii) the exact equilibrium is recovered in the long time limit, and (iii) the folding rate is an upper bound of the exact one. The kinetics is compared to the exact one for a small peptide and then studied for a real protein and a model structure. Applications to downhill folders and pulling are also addressed.