FLIF seems to compress higher but to my knowledge there is no major browser support. AVIF support is scheduled for Firefox 80 and Chrome 85 by the end of this month (August 25).
Nice to note, though, is that FLIF tech will not just be thrown away. FLIF was superseded by FUIF which was then superseded by JPEG-XL. It's doesn't have as great compression in all cases as FLIF, but I'm very optimistic about JPEG-XL being a highly adopted new image format.