Well TIFF has very poor compression leading to large file sizes compared even to PNG. And thus no one uses it on the web.
FLIF has very good compression, it will only download the minimum amount of data required to display the image at it's current resolution. It supports 32-Bit images/animations/transparency. It does animation playback in realtime while it's downloading the file. So as it plays the resolution just increases, you aren't waiting for the next frame to load, only improve. FLIF can also handle the incredibly high resolution images that TIFF is usually used for, and can even do tiled rendering, where it only loads the chunks of the image you are zoomed in at into memory at that resolution. Meaning it takes less time to render those chunks on gigantic images and it uses less memory to do so.
FLIF is an incredibly powerful format that offers a lot. It has archival, scientific, and web purposes. It likely won't be useful to those in 3D or Gaming as files like TGA are better suited for faster reading/loading where as FLIF is a little slower to decompress than PNG. But then again, game devs have been optimizing resource usage for a long time giving models that are further away lower poly counts and lower quality bitmaps/textures. So having one flif image to work at any distant may be of use for them, where they truncate the file at different lengths depending on distance from the camera.
There is a lot to be explored with this format, and it isn't even finalized yet.