If you say 'I'm through with ...' it means 'I'm fed up with ...' 'I've had enough of ...' and I'm not going to be involved with this any more. It means that for me, this is finished.
This use of 'through' is American and informal. The nearest equivalent, if you know the phrase, is 'I'm done with ..'
The singer is saying that from now on, they'll play by their own rules. Or in other words, they'll live their life how they want to.