Hi
Evan Corkrean •,
Welcome to Microsoft Q&A forum and thanks for using Azure Services.
As I understand, you are getting error: "no pg_hba.conf entry error" in Azure Database for PostgreSQL Flexible Server.
Could you please refer to the solutions provided in this Stackoverflow thread and see if this helps in your case:
https://stackoverflow.com/questions/1406025/no-pg-hba-conf-entry-for-host
Let us know if it does not help and share configuration details of your server.
Thanks