The idea is that each of the scheduled events would show up on the map with a driving route (in order). There are websites that can do this, but I know that FileMaker can show a web-portal and put that information in.
Use Google maps api. Google Static Maps Developer Guide | Google Static Maps API | Google Developers
Sample Database Dropbox - GoogleMapSample.fmp12
Will the API allow FileMaker to show the whole route, in order?
Google has different options to display the data you want. The sample I provided will allow you to pin each location on a map.
Maps API: Application Development & Analytics
Retrieving data ...