I either could use the Frame-Sync-Output, capture it with an Arduino and then trigger a flash with it, right? Or I could provide a trigger signal both for the camera and the flash, making the camera expose and the flash trigger.
Either one should work, but if you use the same signal to both expose the camera and trigger the flash, you don't need the arduino, and you can also use the Exposure Trigger or Shutter Gating trigger modes.
If each frame of the camera is triggered by an external source, would it be possible then to make the camera do a speed ramp?
Yes, you can do speed ramps with an external source. With the Exposure Trigger or Shutter Gating set on the Trigger/IO settings screen, the camera will record a new frame with every pulse. The difference between the two is that with Exposure Trigger, the sensor will expose for whatever the exposure time is set to on the camera, and with Shutter Gating, the exposure will last for as long as the signal is high.