FLAC is the audiophile's handshake: CD-perfect sound at roughly half the shelf space. It was born in 2001, Josh Coalson; now kept by the open Xiph.Org Foundation, and its real weak spot is fitting in pockets: lossless is still large: and charming Apple's own apps.
FLV is a relic of the Flash era: the format YouTube grew up on, stranded when Flash died. The Flash Video container, typically holding old H.263, VP6 or early H.264 streams. That makes it the right destination when what you need is nothing new: today it's mostly old downloads waiting to be rescued.