High levels of X-ray and UV activity on young M dwarfs may drive rapid atmospheric escape on temperate, terrestrial planets orbiting within the liquid water habitable zone. However, secondary atmospheres on planets orbiting older, less active M dwarfs may be stable and present more promising candidates for biomarker searches. We present new HST and Chandra observations of Barnards Star (GJ 699), a 10 Gyr old M3.5 dwarf, acquired as part of the Mega-MUSCLES program. Despite the old age and long rotation period of Barnards star, we observe two FUV ($delta_{130}$ $approx$ 5000s; $E_{130}$ $approx$ 10$^{29.5}$ erg each) and one X-ray ($E_{X}$ $approx$ 10$^{29.2}$ erg) flares, and estimate a high-energy flare duty cycle (defined here as the fraction of the time the star is in a flare state) of $sim$ 25%. A 5 A - 10 $mu$m SED of GJ 699 is created and used to evaluate the atmospheric stability of a hypothetical, unmagnetized terrestrial planet in the habitable zone ($r_{HZ}$ $sim$ 0.1 AU). Both thermal and non-thermal escape modeling indicate (1) the $quiescent$ stellar XUV flux does not lead to strong atmospheric escape: atmospheric heating rates are comparable to periods of high solar activity on modern Earth, and (2) the $flare$ environment could drive the atmosphere into a hydrodynamic loss regime at the observed flare duty cycle: sustained exposure to the flare environment of GJ 699 results in the loss of $approx$ 87 Earth atmospheres Gyr$^{-1}$ through thermal processes and $approx$ 3 Earth atmospheres Gyr$^{-1}$ through ion loss processes, respectively. These results suggest that if rocky planet atmospheres can survive the initial $sim$ 5 Gyr of high stellar activity, or if a second generation atmosphere can be formed or acquired, the flare duty cycle may be the controlling stellar parameter for the stability of Earth-like atmospheres around old M stars.
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