Do I need a flyback diode?
I have not personally worked with solid state relays before, but from my understanding they function similar to an opto-isolator, with an LED triggering a phototransistor (or photodiode) into order to close or open the "switch". As such, the triggering side is isolated from the output side so I don't think you need a flyback diode. However, if you are switching an inductive load , you should still have to include a flyback diode or other snubber circuitry on the output side to avoid damaging the load.

Looking at the "Standard" circuit for using one of the Sharp S108T02/S208T02 SSRs, they have included a diode across the input pins, but I believe this is just to avoid exceeding the maximum reverse voltage of the internal LED (which for that particular device is only 6V). The specific datasheet for those SSRs can be found here.