PLANETS TRANSITING VERY NEARBY SMALL STARS OFFER THE BEST OPPORTUNITY TO OBSERVE THE ATMOSPHERES OF ROCKY PLANETS ONE OF THE MAJOR GOALS OF THE JAMES WEBB SPACE TELESCOPE (JWST). HOWEVER WE DO NOT CURRENTLY UNDERSTAND THE HIGH ENERGY OUTPUT OF M DWARFS WELL ENOUGH IN ORDER TO INTERPRET SPECTRA OF THE TERRESTRIAL WORLDS AROUND THEM. IN OUR SOLAR SYSTEM HIGH ENERGY RADIATION FROM THE SUN HAS SCULPTED THE ATMOSPHERES OF THE SOLAR SYSTEM'S ROCKY PLANETS AND MOONS DESICCATING SOME WHILE SHROUDING OTHERS IN HAZES. HIGH ENERGY EMISSION FROM M DWARFS MAY SHAPE THEIR PLANETS' ATMOSPHERES EVEN MORE PROFOUNDLY AS THESE WORLDS LIE MUCH CLOSER TO THEIR PARENT STAR THAN THE SUN'S PLANETS LIE TO IT. HERE WE PROPOSE TO USE THE CAPABILITY OF TESS TO COLLECT CONTINUOUS OPTICAL PHOTOMETRY AT OPTICAL WAVELENGTHS IN ORDER TO MEASURE THE OCCURRENCE RATE AND STRENGTH OF STELLAR FLARES FROM THE PLANET-HOSTING M DWARFS GJ 1132 AND LHS 1140. BOTH GJ 1132B AND LHS 1140B ARE TERRESTRIAL PLANETS DISCOVERED BY THE MEARTH SURVEY AND BOTH TARGETS ARE CURRENTLY PLANNED TO BE OBSERVED WITH JWST AS PART OF THE GUARANTEED TIME OBSERVATIONS (GTO) PROGRAMS.