  We analyze the two brightest Chandra X-ray flares detected from Sagittarius
A*, with peak luminosities more than 600 x and 245 x greater than the quiescent
X-ray emission. The brightest flare has a distinctive double-peaked morphology
--- it lasts 5.7 ksec ($\sim 2$ hours), with a rapid rise time of 1500 sec and
a decay time of 2500 sec. The second flare lasts 3.4 ksec, with rise and decay
times of 1700 sec and 1400 sec. These luminous flares are significantly harder
than quiescence: the first has a power law spectral index $\Gamma = 2.06\pm
0.14$ and the second has $\Gamma = 2.03\pm 0.27$, compared to $\Gamma =
3.0\pm0.2$ for the quiescent accretion flow. These spectral indices (as well as
the flare hardness ratios) are consistent with previously-detected Sgr A*
flares, suggesting that bright and faint flares arise from similar physical
processes. Leveraging the brightest flare's long duration and high
signal-to-noise, we search for intraflare variability and detect excess X-ray
power at a frequency of $\nu \approx 3$ mHz, but show that it is an
instrumental artifact and not of astrophysical origin. We find no other
evidence (at the 95% confidence level) for periodic or quasi-periodic
variability in either flares' time series. We also search for non-periodic
excess power but do not find compelling evidence in the power spectrum. Bright
flares like these remain our most promising avenue for identifying Sgr A*'s
short timescale variability in the X-ray, which may probe the characteristic
size scale for the X-ray emission region.
