AWS ECS container logs design pattern
When using docker, the recommended approach is to not log to files, but to send logs to stdout and stderr. Doing so prevents the logs from being written to the container's filesystem, and (depending on the logging driver in use), allows you to view the logs using the docker logs / docker container logs subcommand.
Many applications have a configuration option to log to stdout/stderr, but if that's not an option, you can create a symlink to redirect output; for example, the official NGINX image on Docker Hub uses this approach.
Docker supports logging drivers, which allow you to send logging to (among others) AWS cloud watch. After you modified your image to make it log to stdout/stderr, your can configure the AWS logging driver.
More information about logging in Docker can be found in the "logging" section in the documentation
You don't need log agent if you can change the code.
You can directly publish Custom Metric Data into ColudWatch like this page said: https://docs.aws.amazon.com/sdk-for-java/v1/developer-guide/examples-cloudwatch-publish-custom-metrics.html