Why are these flickering lines appearing during a fade to black in my Premiere render?
I believe what you reference is called "artifacts".

Those phenomenons are a result of compression. Vimeo does not use the raw file you upload as playback. Instead, the file is converted and compressed for storage-purposes mainly. This might be one reason as of why this is appearing.

The second possibility is that your footage was not recorded at a deep-enough bitrate, and so it seems from the information you gave. h.264 is always a lossy codec, which means that you're gonna throw away a chunk of data when writing a file in h.264. I know that the gh5 is able to record in avchd, which would be a far better choice in terms of image quality compared to mov h264 or mp4 h264. Try recording in that format.

Lastly, using a flat profile could safe you some extra-information in those parts that get compressed could help you. The gh5 has a vlog-L profile as well as a Cinelike D one. These are so called "flat profiles" which will lower the contrast and saturation at first, but give you the ability to adjust contrast and brightness afterwards. Recording in a flat profile captures more information in very bright or very dark areas, which would otherwise get lost. Trying this might also improve your results.

However, Vimeo, youtube, Clipfish, hell what ever Streaming-Service you use - compression will take place, which means that your video will look worse there than in the original file. Depending on what you're planning on the long run (for example sending a video to a client) it might be a better idea to straight up upload the prores4444 or DNxHR or similar near-lossless codec and send the link to the client (for example via ftp-server) so he/she/it can download it directly without the use of 3rd-party streaming-services.

Hope my answer was helpful, happy filming!