I agree with Katy's answer that in quite formal contexts even individual contractions are frowned upon. But, since you ask about double contractions, you may be interested in writing that is informal enough that contractions are acceptable, but still somewhat formal. And, generally, your intuition is valid that doubling up contractions increases the informality. For instance, a news article about trade negotiations is generally written in a fairly formal style, but contractions are often shown in quoted speech. But, if someone said "wouldn't've" out loud, that would show up as "wouldn't have" in the article.
On the other hand, the way you write dialogue in a novel is part of your style. You may want to convey more about how the speech is being delivered than what comes across in standard, cleaned-up prose. I would still advocate restraint. Complicated contractions, like dialect respellings, tend to stand out and can distract the reader.