How Do I Bring Up That I Want a Breast Reduction?

I really think you should tell him that you have a medical problem for which you need to see a doctor. Schedule a consultation with your physician, pediatrician, and or gynecologist first and discuss it with them.  Review your medical symptoms such as neck, back and shoulder discomfort, limited physical activity, rashes in breast crease, etc. Also I would agree with searching for medical articles to show your dad after the physician's examination and recommendation.

This is a conversation you should have with your parent.  Obviously until you are 18 or older you can not have this done without  your parent's permission.