  We present the second catalog of flaring gamma-ray sources (2FAV) detected
with the Fermi All-sky Variability Analysis (FAVA), a tool that blindly
searches for transients over the entire sky observed by the Large Area
Telescope (LAT) on board the \textit{Fermi} Gamma-ray Space Telescope. With
respect to the first FAVA catalog, this catalog benefits from a larger data
set, the latest LAT data release (Pass 8), as well as from an improved analysis
that includes likelihood techniques for a more precise localization of the
transients. Applying this analysis on the first 7.4 years of \textit{Fermi}
observations, and in two separate energy bands 0.1$-$0.8 GeV and 0.8$-$300 GeV,
a total of 4547 flares has been detected with a significance greater than
$6\sigma$ (before trials), on the time scale of one week. Through spatial
clustering of these flares, 518 variable gamma-ray sources are identified.
Likely counterparts, based on positional coincidence, have been found for 441
sources, mostly among the blazar class of active galactic nuclei. For 77 2FAV
sources, no likely gamma-ray counterpart has been found. For each source in the
catalog, we provide the time, location, and spectrum of each flaring episode.
Studying the spectra of the flares, we observe a harder-when-brighter behavior
for flares associated with blazars, with the exception of BL Lac flares
detected in the low-energy band. The photon indexes of the flares are never
significantly smaller than 1.5. For a leptonic model, and under the assumption
of isotropy, this limit suggests that the spectrum of the freshly accelerated
electrons is never harder than $p\sim$2.
