It should work if the flash is directly connected to the camera via the hot-shoe or via an appropriate off camera cable.
I believe the flash is old enough that it was made for the Olympus DSLRs and not the micro 4/3rds cameras. The one incompatibility is those flashes had a red focus assist light that the cameras could control. The micro 4/3rds cameras do not use this light.
FWIW, the newest micro 4/3rds bodies and flashes now support a white focus assist light that can double as a video light, but this flash doesn't have it.
The flash supports being a flash slave. Depending on the Panasonic camera (I don't know the Panasonic line like I do the Olympus line), it may be useful if you are going to do manual flash shots. The problem is the older Panasonic bodies did not support a manual flash mode for the pop-up flash. The flashes that support being a slave typically needs the camera to have a manual flash, because the flash fires on the first pulse. If the camera does not have a manual flash mode, the camera will fire a test pulse to figure out how much lighting is needed, and the slave flash will trigger on that. Newer Panasonic bodies now support a manual flash mode (my G85 has it).
I believe the flash does not support the remote flash protocol that Olympus cameras use (and recent Panasonic cameras) that allows the camera to do TTL control of the flash remotely. This means you are limited to using the flash in manual flash setting.
Just a final note about Olympus flash compatibility. Olympus has gone through 4 major flash iterations. The original flashes were for the film cameras and are only useful on micro 4/3rds cameras as a strictly manual flash. Usually the flash name started with G-*. And really old film flashes can be camera killers, sending hundreds of volts through the hot-shoe.
The second generation was the early digital cameras (E-10, E-20, C-* cameras). This flash was the FL-40, and it is not compatible with the current cameras.
There was an intermediate flash (FL-20) that was paired with the SP-350. It wasn't compatible with the FL-40. Olympus cameras keep compatibility with the FL-20, but Panasonic cameras don't.
Then the modern generation (FL-36, FL-50). All Panasonic micro 4/3rds cameras should be able to use these flashes with the flash in the hot-shoe.
After a bit, Olympus introduced the R flashes (FL-36R, FL-50R, FL-300R, FL-600R, FL-900R) that can do off camera TTL, using the camera's built-in or clip-on flash to act as a flash master, sending out coded signals to control the flashes. Panasonic only started supporting the R flashes in the last few years.