As I have said there are multiple ways to do this. What is the most logical way its up to you... When using cp_log_export tool after adding the log export just restart the added export and it will start exporting the logs. Ensure that necessary ports are open (e.g. Azure NSG's or AWS SecurityGroups where the Syslog is located).
cp_log_export add name to_RemoteServer target-server X.X.X.X target-port 514 protocol udp format syslog
cp_log_export restart name to_RemoteServer
After what you do from the syslog its up to you and DataDog agent 🙂