Does a solid-state DIN relay typically need a flyback diode when switching an inductive load?
No, I don't think so. The diode has to go across the load so there would have to be another pin.
You'll need to add an external diode across the load.
Whatever that reference to &quot;free wheeling diode&quot; means, it is in the input section of the datasheet. There is also nothing shown in the schematic.

A 1N400x eg. 1N4004 etc. 1A diode is more than sufficient for this application.