Indeed FM supports loading DITA files (I tried FM10 and newer) but to automate conversion to .FM format you either use the internal scripting mechanism which is still some manual work.
I have found an existing free utility that can do most basic operations like opening a file, 'saving as' another format and closing it.
tool name is DZBatcher
Example DZbatcher batch file:
Open "c:\My Dita Files\Doc1.dita"
SaveAs -d "c:\My FM Files\Doc1.fm"
Close "c:\My FM Files\Doc1.fm"
Open "c:\My Dita Files\Doc2.dita"
SaveAs -d "c:\My FM Files\Doc2.fm"
Close "c:\My FM Files\Doc2.fm"
Exit
Adobe has a framework called RoboHelp which is probably the infrastructure for this, but I didn't dig deeper as this utility did the job perfectly.
In my SW flow, I created this batch file using a python script that scan all the docs in an input directory and added 3 lines per file as seen above.
I used FM2015 for this task.