  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.
