What is incumbent upon someone who vowed to fast three days for each time they committed a specific sin, and they have committed it 15 times? Is expiation (kaffara) obligatory for all those instances, and is there a way to annul this vow in the future?

You must repent to Allah Almighty for the sin, while being mindful of His greatness and power. If no vow was uttered, then nothing is binding, because a vow is not contracted except by utterance. If you uttered a word that implies commitment, then it is a vow of obstinacy (nadhr lajaj), and you have the choice between fulfilling it or offering an expiation for an oath (kaffarat yamin). If you do not wish to fulfill it, then you must offer an expiation for an oath (feeding ten poor people, or clothing them, or freeing a slave). If you are unable to do so, then you must fast for three days, and it is more prudent for them to be consecutive.