I'd suggest just poking around in these first:
http://io.livecode.ch/ online interactive minikanren examples
http://tca.github.io/veneer/examples/editor.html more minikanren examples.
You already mentioned http://minikanren.org/ You may also want to check out the book The Reasoned Schemer.
I did a slightly faulty implementation ( I didn't get the search ordering right) in Julia here https://www.philipzucker.com/yet-another-microkanren-in-juli...
Microkanren implementation tutorial https://www.youtube.com/watch?v=0FwIwewHC3o . Also checkout the Kanren online meetup recordings https://www.youtube.com/user/WilliamEByrd/playlists