I'm sure that there are several ways to do it. The easiest would be to create a shell script that scans the Log directory under BatchServer and emails any new files. Question is why you want do this. Usually reading log files is an adhoc activity initiated by errors or other signals.
Continues monitoring can done via Environment Manager, much better than browsing individual logs. On a job/flow level, the flow log under the SchedulingManager directory is more user friendly. As stated earlier, checking logs for errors is a signal initiated activity. When receiving a such, one could easily check the og on the server. Mailing all logs makes little sense, especially in large deployments.