you can write a system level script that will copy the contents of the filemaker logs folder to a remote location.
For instance, you can add a text file called copy.bat to the scripts directory under C:/Program Files/Filemaker Server/Data/Scripts/ that has a powershell script of:
robocopy "C:\Program Files\Filemaker Server\Logs" "\\syslogserver\logs" /MIR
This will mirror anything from the filemaker server logs directory over to a network machine called "syslogserver" into a "logs" shared folder.
Then you set up a schedule in the filemaker server control panel that runs that copy.bat system level script at whatever interval you want.
Thanks for the idea Mike. I'm running an OSX system and was wondering if there was a way to integrate it with syslogd.