Liar-soft Fanclub Magazine "Gekkan Uso" (Monthly Lie)
Contrary to its name, this was a quarterly print publication issued by Liar-soft to its paid fanclub members.
As part of its run, the magazine had a multi-page advertisement for Kindred Spirits (available untranslated here), five issues of a Kindred Spirits illustration + Q&A column, one segment detailing the school's history, and an advertisement for the first drama CD, as well as a segment about the school cafeteria.
Additionally, Kindred Spirits characters were featured in some magazine illustrations (including a celebratory illustration for volume 50) and a two of the ending comics. Reports of a June 2019 fanclub mailing containing a 1koma featuring Sachi and Megumi also exist, but I'm unaware of any further details.
There was also a "Letters & Points" column where fanclub members could submit letters and fanart about different Liar-soft games (Kindred Spirits included) and get a response from staff. I'm not planning to seek out issues specifically for these columns, but I've included relevant entries when they pop up in the issues I have.
Gekkan Uso (Monthly Lie)
Kindred Spirits Content
BugBug Magazine
For some months after the game's release in 2012, Kindred Spirits' publisher, Liar-soft, ran multiple articles in the eroge advertisement magazine BugBug.
This included a corner introducing the game (untranslated, but including a short story that has been translated), a short colored manga, and a number of illustration columns.
As a precaution, do note that some of the art in these columns is quite suggestive.
BugBug Magazine
Kindred Spirits Content