Can you deploy your app successfully? Is this error received when you try to connect to your app? Very likely, your app does not complete the request-related work within the defined deadline. A request handler has a limited amount of time to generate and return a response to a request, typically around 60 seconds. Once the deadline has been reached, the request handler is interrupted. The Java runtime environment interrupts the servlet by throwing a com.google.apphosting.api.DeadlineExceededException. If the request handler takes more than a second after raising the exception to prepare a custom response, a HardDeadlineExceededError will be raised. Both DeadlineExceededExceptions and HardDeadlineExceededErrors will force termination of the request and kill the instance. You may find more detail in the "Specifying a request deadline"
sub-chapter of the "How Requests are Handled" online document.
A relevant sample of your Cloud SQL related code is needed to identify the possible source of the delays.
What is the output of the gcloud info command on your development machine?