For a while this was a thing and still is to a degree. Not directly in DNS so to speak, but in whois.

    whois ycombinator.com|grep -Ei "phone|email"
       Registrar Abuse Contact Email: [email protected]
       Registrar Abuse Contact Phone: +33.170377661

This used to be a way to get contact information for domain holders but spammers have effectively squashed that concept. Phone numbers are also commonly stored in LDAP/AD databases and can be queried over DNS internally within an organization.

If one were so inclined they could share their contact information in DNS in TXT records. Not many people would know to query this unless it became a standard at which point spammers would squash it there as well.

Another semi-standard domain related place people could put contact information if they were so inclined is humans.txt [1]

[1] - https://www.python.org/humans.txt