it could work with a nikon f-mount (d3300) to sony e-mount( a7iii). 

Yes, it will fit any Sony e mount body, either full frame (a7..., a9...), or aps-c (like a6500, etc) 

No the other way this is to be able to mount the Nikon lenses onto the micro 4/3 camera body 

There are 6PCS adapter ring included in this flash, here is the size:
52 55 58 62 67 77mm, as long as your lens size is one of them, then could be used,
Here is the way to check your lens size:
Your camera's lens thread size will be marked somewhere on the lens barrel or printed underneath your lens cap. This number is always preceded by a "?" (diameter) symbol. For example: ?52 = 52mm lens thread size.
If your lens size is none of them, please tell us, we may include the size you need but at this case, this item must be shipped from China so that we could pack with this adapter ring you need. 

You should order one for every manual Nikon lens you want to use with you Sony mirrorless camera.