"We are not listening to them."
Translation:My ich nie słuchamy.
The most natural way to say it is probably "Nie słuchamy ich". My next choice would be "My ich nie słuchamy", which emphasizes 'we' by putting it explicitly in the sentence. And basically those are the only two word orders I would use here.
"Ich nie słuchamy" is like "Them we do not listen to". Very strong and really not natural emphasis on 'them'. Basically, putting a pronoun in a different case than Nominative at the beginning of the sentence is rarely natural.