Because of Shinki's dialogue in which she mentions that everything in Makai is her creation, it is a popular theory that Alice is Shinki's daughter. However, there's been no further mention of this since then, and Perfect Memento states that Alice was once a human who became a youkai magician. It is unknown whether this is a retroactive change of continuity, merely a mistake by Akyu, or if fans were mistaken from the beginning when thinking Alice was Shinki's daughter.
A speculation about it has been permitted into a particular doujin Ear House, Grimoire of Alice, Which assumes that Alice has been adopted by Shinki, then turned into a youkai in the Mystic Square Extra Stage. But all this is obviously only speculation.
Fans have interpreted her hairstyle to be an ahoge, literally "idiot hair", which influences fanon portrayals.
Many fans thought Shinki was going to appear in Undefined Fantastic Object because the setting was in Makai. Fans were very disappointed after Shinki didn't appear and wasn't even mentioned in Undefined Fantastic Object.
Some fans speculate that Shinki has a relationship or acquaintance with Byakuren Hijiri as it's shown in fanart, sometimes suggesting that Shinki taught Byakuren some of her attacks.
This theory might be to calm down the controversy of Byakuren's usage of Shinki's attack pattern, as many fans were expecting Mima or Shinki to make an appearance in the Windows games after being practically forgotten about. Seeing Byakuren use Shinki's attack offended them.