This dialect is referred to as African American Vernacular English, and it does in fact have its own set of internally consistent rules for such things.
One thing you have to realise here is that
done in your sentence is used as an intensifier. It is saying that the action is not meerly completed, but authoratativly so. No doubt about it whatsoever. There isn't really an alaogous commonly-used intensifier for not being done.
ain't is a perfectly legitimate word in this dialect when negation is intended, and it also is used as sort of a mild intensifier.
So the simplest answer would be "He ain't done..."
One note of caution. Often dialog in moves and TV is not written (or delivered) by fluent AAVE speakers, so sometimes they get some of the details wrong. For instance, AAVE present tense verbs often lose inflection (eg: a trailing
eat above is being used in the context of past tense. It feels wrong to me, but my AAVE is admittedly a bit rusty.