@Josh Ondayko avatar imageJoshOndayko-0323 Thank you for posting your query on Microsoft Q&A.
My understanding is that stopping a flexible server on Azure MySQL Database is taking longer than expected. Please let me know if my understanding is not correct.
I was able to test this from my end and I was able to start and stop MySQL flexible server without any issues. The location I am using is East US. Could you please try again later and let us know if the error occurs again? As an alternative you can also use CLI code to stop the server.
Start and stop an Azure MySQL Flexible server
If this still occur, then the best route will be to create a support ticket so we can further investigate at the back end.
Regards,
Oury