From what I can glean, it'll and I've exist as standard contractions, but I am unsure of whether it'll've either exists or is acceptable.
"It will have" should be able to be reduced to "it'll've", shouldn't it?
It is true that "it will have" (or "it'll have") is usually reduced in pronunciation to something that might arguably be better represented in writing is "it'll've".
But not every such reduction is standardly represented in writing. For example, the standard spelling is to write "would have", even though the vowel of "have" is usually pronounced as a schwa. Hence one might argue that it would be perfectly logical to spell this "would've", just as it would be perfectly logical to spell "women" as "wimmin": perfectly logical, just not the standard spelling.