The Lumix G6 supports the Olympus wireless flash protocol, the first of the G series to do so, which enables a compatible flash to be used on or off the camera. Although it is called wireless, it's really an optical light system and will not work in bright light and depends on line of sight. There is no true simple radio transmitter system available like those readily available for Canon or Nikon. I use an Olympus 36R and 2 X M/43 dedicated Metz 48 AF-1 flashguns, all bought secondhand and all work perfectly. All support High Speed Sync (FP TTL in Olympus speak) and can be used off the camera using the built in flash to set off the remotes.
I use the Olympus 36R with my Olympus Pen, it's small and doesn't upset the balance of this small camera too much. Recycle time is quite slow though as it only has 2 batteries. The Olympus 36 and 50 non R versions do not support off camera use but go for less money compared to the R version.
I really like the Metz flash guns, quite simple to use and typically much cheaper secondhand compared to Olympus/Panasonic offerings and I use them with my GH3. I think that the AF 48 and upwards all offer HSS and remote slave cabability and user upgradable firmware, I have upgraded both of mine to the latest version via the mini USB socket. Anything below the AF 48 series loses functionality. They use 4 batteries and so the recycle time is much better than the 36R.
Other options are the very expensive Olympus 50R and Lumix equivalent and Nissin. I personally have no experience of these and the Nissin is too recent to fall within my budget.