In lossless compression, it beats TIFF hands-down for the mainstream compression methods (packbits, LZW, ZIP). You can use pretty much whatever compression you want in a TIFF file (it's more of a container format than an encoding definition), but given how well FLIF compresses vs other image compression methods, it's pretty good.
The progressive loading is also superior to TIFF, which generally don't use progressive at all. I'm not sure how much this matters, though, as their example of using it for responsive design assumes that the graphic at lower resolutions 'as is' gives an acceptable enough result to replace current solutions that serve a different resolution image that may well have been specifically tuned for a given resolution/bandwidth. JPG already has similar progressive loading, and I don't know of any browser that will halt a JPG download after the Nth iteration deeming it 'good enough'.
It also apparently has animation support, which may be better than APNG and MNG and others. For now GIF still seems to rule the animated image domain, despite its many shortcomings (imgur's faked-out video -> gif -> mp4-served-via-html-named-gifv doesn't count).
On most other fronts, though, it seems TIFF (and other formats) may be superior. A rather big one is that it doesn't yet support metadata. Another big one for the graphics industry would be lack of CMYk and other color spaces.
It also seems to support 'only' 16 bits per channel. There's a variety of 32bpc encodings for TIFF (straight, LogLUV, etc) and I do hope that it's just an arbitrary limit such that the work done in FLIF could conceivably be added to formats like OpenEXR.
That would also largely take care of concerns like the lack of additional channels, layers, etc. that can be presented in TIFF. This would make OpenEXR the container format and FLIF the encoding (or, at least, the compression).
That would still place it squarely in the interest of those dealing with graphics (a very fast decode of the progressive version used when framescrubbing, then loading the full 10k plate when paused for a bit, for example), and not so much the average consumer.
For consumer adoption, it would need broad support among browsers (lack of webp support means that hasn't particularly taken off), from digital imaging device manufacturers (you're more likely to upload 'a FLIF file' if that's what rolled out of the camera / got written to the SD card to begin with) and in common software (but that tends to follow from the other two).