You could try reaching out to the VA and obtain his records if he received any treatment. They will have discharge papers in their files. Also you can try reaching out to your states veterans office for help, some states recorded discharge papers. Some county veterans offices also recorded discharge papers at the county clerks office. Many soldiers did this when getting out of service.
If you are seeking to obtain his full military file you will have to submit a request. However, at this current time they are only processing emergency requests for education, medical, and home loans.
For requesting records, medals, and awards please use eVetRecs on NARA’s website at https://vetrecs.archives.gov/VeteranRequest/home.html or complete a GSA Standard Form 180 and send it to NARA's Military Personnel Records, National Personnel Records Center, 1 Archives Drive, St. Louis, MO 63138-1002.
Dear Ms. Dailey,
Thank you for posting your request on History Hub!
We suggest that you request a copy of his Official Military Personnel File (OMPF). OMPFs and individual medical reports for those who served in the U.S. Armed Forces during the Vietnam War are in the custody of NARA's National Personnel Records Center in St. Louis. In many cases where Army and Air Force personnel records were destroyed in the 1973 fire, proof of service can be provided from other records such as morning reports, payrolls, and military orders, and a certificate of military service will be issued. Navy and Marine Corps OMPFs were not affected by the fire. Please complete a GSA Standard Form 180 and mail it to NARA's National Personnel Records Center, (Military Personnel Records), 1 Archives Drive, St. Louis, MO 63138-1002. For more information see Request Military Service Records.
Due to the COVID-19 pandemic, the NPRC was closed from March 23 through June 23, 2020. As of June 24, the NPRC entered into Phase One of a gradual reopening process. On October 5, NPRC entered Phase Two. The center currently is only servicing emergency requests associated with medical treatments, burials, homeless veterans, VA Home loan guarantees, and employment opportunities. If this is urgent, please see Emergency Requests and Deadlines. We apologize for any inconvenience.
We hope this is helpful.