We present a study of white-light flares from the active M5.5 dwarf Proxima Centauri using the Canadian microsatellite Microvariability and Oscillations of STars. Using 37.6 days of monitoring data from 2014 to 2015, we have detected 66 individual flare events, the largest number of white-light flares observed to date on Proxima Cen. Flare energies in our sample range from 1029 to 1031.5erg. The flare rate is lower than that of other classic flare stars of a similar spectral type, such as UV Ceti, which may indicate Proxima Cen had a higher flare rate in its youth. Proxima Cen does have an unusually high flare rate given its slow rotation period, however. Extending the observed power-law occurrence distribution down to 1028 erg, we show that flares with flux amplitudes of 0.5% occur 63 times per day, while superflares with energies of 1033 erg occur ~8 times per year. Small flares may therefore pose a great difficulty in searches for transits from the recently announced 1.27 M ⊕ Proxima b, while frequent large flares could have significant impact on the planetary atmosphere.