Double contractions like this don't occur in standard print. I do sometimes use it.

My rule of thumb is to do it if it's needed to show what I say. Written "I have" is pronounced as two distinct words: I don't read it as "I've". Nor do I read "do not" as "don't".

But given written "I'd have", I'd pronounce it as "I'd've", not (normally) with a distinct "have". So there's no need to supply the second contraction in writing, when the standard form "I'd have" is pronounced in the way you want.

That said, I've noticed my use of "I'd've" is increasing, when I'm writing more colloquially.

In the same way, I might write "Elizabeth'll do it", where in serious print you only get pronoun + contraction.