You could just truncate the file at x% and get lossy encoding that way.
However, truncated FLIF files will (probably) never achieve the same quality/size ratio as dedicated lossy methods that can produce a completely different file for each quality setting.
So at the moment I still see an important use case for lossy methods. However, in the future, I can imagine that people will start to demand/expect lossless encoding, to avoid generation loss and to get the most out of their display hardware. E.g. higher bit depths are becoming a thing, while the JPEG/WebP color space (YCbCr) is effectively less than 22 bits per pixel (roughly speaking, red and blue are only 7-bit), and chroma subsampling makes this even worse. Also what's the use of ever higher display resolutions if most of those pixels are only displaying compression artifacts or blur? Lossy formats like JPEG/WebP/BPG/JP2/JXR are good at medium-quality, but if you use them at a near-lossless quality setting (e.g. 99 or 100 for JPEG), they often produce bigger files than lossless formats.
Meanwhile, the range of display sizes is getting larger: while in the past, we had a range from say 13" monitors to 21" monitors, now we have a range from 1.5" smart watches to huge 100" smart TVs. I do think that in order to avoid huge amounts of rescaling/transcoding, we need image/video formats that are "responsive by design", like JPEG2000 and FLIF (and progressive JPEG to some extent).
Writing out the detailed spec is going to take some effort.
For lossy movies, actual video codecs are best, since they're designed for that. BPG is essentially HEVC (a great but patent-encumbered video codec) so it should be good at lossy movies -- it will be worse on line-art animations with hard edges like e.g. cartoons, or animations with transparency.