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 $6sigma$ (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 $psim$2.
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