Get the logs of "shinylogs" package exported to cloudwatch

Dear Team,
We have a shinyproxy application running on EKS with 2 applications. We want to export the container logs using fluentbit to AWS cloudwatch. The stderr and stdout are working fine since they are created in the proxy container.
We are using one more package called shinylogs and this package creates logs in the application container and the log file is only created after the session timeouts and somehow fluentbit is not exporting these logs to cloudwatch.
Could anyone help here?