Phased flaring, or the periodic occurrence of stellar flares, may probe electromagnetic star-planet interaction (SPI), binary interaction, or magnetic conditions in spots. For the first time, we explore flare periodograms for a large sample of flare stars to identify periodicity due to magnetic interactions with orbiting companions, magnetic reservoirs, or rotational phase. Previous large surveys have explored periodicity at the stellar rotation period, but we do not assume periods must correspond with rotation in this work. Two min TESS light curves of 284 cool stars are searched for periods from 1-10 d using two newly-developed periodograms. Because flares are discrete events in noisy and incomplete data, typical periodograms are not well-suited to detect phased flaring. We construct and test a new Bayesian likelihood periodogram and a modified Lomb-Scargle periodogram. We find 6 candidates with a false-alarm probability below 1%. Three targets are >3-sigma detections of flare periodicity; the others are plausible candidates which cannot be individually confirmed. Periods range from 1.35 to 6.7 d and some, but not all, correlate with the stellar rotation period or its 1/2 alias. Periodicity from 2 targets may persist from TESS Cycle 1 into Cycle 3. The periodicity does not appear to persist for the others. Long-term changes in periodicity may result from the spot evolution observed from each candidate, which suggests magnetic conditions play an important role in sustaining periodicity.
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