I'd also consider WebP. FLIF is great but compression time is much slower than WebP for similar results.

Store it as FLIF then dynamically serve up whatever is needed for the web interface...

We're storing them as RAWs for our backups, but it's cheaper and faster to store them compressed and transmit them without a transformation step. I'll keep FLIF in mind, but it looks kind of unstable reading the website?

Yes, the FLIF format is still being fully fleshed out. I would actually give WebP a shot instead of JPG. It offers better compression and already has native implementations in Chrome and on Android.