If your playlist doesn’t have a Share button, it can be for two reasons:
A track in the playlist is stuck in transcoding
If you have uploaded multiple tracks in a playlist, it may be that one of them did not successfully upload all the way. You’ll be able to see this, as the individual track’s waveform will be grayed out and it cannot be played.
If this has happened, please delete the track from SoundCloud and upload it again. From there, you can add the track into the playlist afterwards. You can learn more about how to do this here.
A track in the playlist does not have embeds enabled
If all of the tracks in the playlist are fully transcoded and available to play on Soundcloud and you are unable to see a Share button on your playlist, you should look to make sure all tracks in the playlist have embeds enabled. You can test this by checking at each track individually, and making sure they have individual Share buttons.