Do what they say. Use the eVetRecs service. I faxed my signature.
A few weeks later, 2 copies of my DD 214 with a frigging seal embossed arrived first class.
Can it be any easier.
So, if your parent can't find their Certificate of Release or Discharge from Active Duty, Report of Separation or Certification of Military Service (or whatever the heck they called it back when), I would highly suggest you help your relation avoid any issues before it becomes a problem (like verifying eligibility with the Veteran Administration medical (VHA) or benefits (VBA) such as burial honors).