Should I promise to keep a safeguarding disclosure confidential?

No. You should not promise secrecy.
Listen calmly, take what the person tells you seriously and explain appropriately that you may need to seek advice or share information to help protect them. Any factual record you make should be kept secure.
If you're unsure how to respond to a disclosure, contact the DIA Helpdesk:
https://www.driving.org/help/