SeedCode and 360Works as well as others offer sync tools for this purpose.
I can recommend 360Works MirrorSync that have worked great for me in several projects for syncing data
Seems filemaker not support iCloud, is that right?
No, you can use iCloud to move your files. iCloud does not sync your file / database.
Steps to move database to iPhone. Ipad will be similar.
1. In FMGo Select Device
2. Select the download icon. Folder with the downarrow
3. Locations defaults to iCloud Drive
4. Select the database you want to copy to FMGo.
Steps to move database from iPhone to iCloud Drive
1. Select Device
2. Select the action icon the icon look like square paper with corner folder and check mark in center.
3. Select the desired database
4. Select the upload icon. The icon with the up arrow.
5. Select the add to iCloud Drive.
Use one of the solution already mentioned above or FMEasySync: A FileMaker Sync Framework to sync your database. Note : Tim does not support FMEasySync.