Spring Boot uses Logback directly by default. It can also be configured to use Log4j 2. It sounds like you want to use a custom logging implementation instead of Logback or Log4j 2. To do that, I think you'd need to write your own LoggingSystem and configure your app to use that LoggingSystem.
https://docs.spring.io/spring-boot/docs/current/reference/html/boot-features-logging.html#boot-features-custom-log-configuration
More details on LoggingSystem here.
https://docs.spring.io/spring-boot/docs/current/reference/html/howto-logging.html
and of course you can reference the Logback / Log4j 2 implementations of LoggingSystem here.
https://github.com/spring-projects/spring-boot/tree/2.0.x/spring-boot-project/spring-boot/src/main/java/org/springframework/boot/logging
Hope that helps!