Analysing "Ain't got no use for no coal company"

The use of "no use for no coal company" is a classic example of a double negative resulting from a attempt to be emphatic.

The subject is an implied "I", and a more grammatical version would be, "I haven't any use for the coal company.", since only a single coal company has been showing interest in her land. A more emphatic and general version, reflecting her disdain for coal mining in general would be "I haven't any use for any coal company".

Well, actually it might be considered grammatical, since it's actually a triple negative, rather than a double negative, and so the negative overall meaning is preserved.

• Ain't got no use for no coal company

This sentence has been done several things to.

The first thing is removing the subject "I" by Conversational Deletion.

The second thing is using idiomatic got to mean have.

The third thing is using ain't (instead of haven't) as a negative of got in this sense.
(actually, that's two things - ain't is dialectal, and be is the wrong auxiliary verb anyway)

The fourth thing is applying Negative Concord instead of Negative Polarity.
That means using extra, non-cancellable negatives to emphasize negation, instead of NPIs like any.

Many dialects of American English, including AAVE, use ain't with got, and use negative concord for emphasis. So it's grammatical, but it's not standard. It's local, and therefore more heartfelt.