I'm getting some pictures from an artist's Discord. It's an invite-only server (the artist had the invite link publicly on another website), so do I use that as the source link? If so, do we use a direct link to the picture, to the message with the picture, to the channel, or something else?

Discord no longer supports permanent links. Eventually, any image you link from discord will be removed by discord itself. Server invites are likewise impermanent.(Even if they are set to never expire, they totally do, discord is not super stable.)

When I get an image from eroborne or his discord directly, I just say so in place of the source. It may not be the best option, but no one complained yet.

Simpler solution: Ask the artist how they'd like to be credit for the source link. afaik, they are NOT required to be filled in, either. It's just good practice to IF you have a source link like a pixiv, or whatever.