I have an application that has 14 different services. Some of the services are dependent on other services. I am trying to find a good way to deploy these in the right sequences without using thread sleeps.
You can use the readiness probe to hit health check APIs of your application which is being deployed and in those health check APIs you can test the other service pods availability by hitting their APIs or service
This is not how Kubernetes works. You can kind of shim it with an initContainer that blocks until dependencies are available (usually via kubectl in a while loop, but you get fancy you can try using --wait).
But the expectation is that you set up your applications to be "eventually consistent" when it comes to inter-service dependencies. In practical terms, this usually means just crashing if a dependent service isn't available, and it will just be restarted until things succeed.