Hello,
Welcome to ehealthforum and thanks for writing
Brown discharge can be due to various reasons as hormonal imbalance,perimenopausal changes,underlying cause as fibroids,cervicitis,polyps etc.
If you have already acheived menopause and later having brown discharge then it could be indicative of underlying issue.It would require a pelvic examination and investigation as Pap smear to rule out the exact cause.
Though breast cancer and discharge might not have any corelation but it is better to get evaluated once.Kindly visit a Gynaecologist for pelvic examination and if required she might advice vaginal smear test for precise diagnosis.Considering your age Pap should be done on a regular basis.
Take care!