After a few hours of messing around, I have finally managed to do it successfully.
@GusAragn @Rootzilla I literally had the same problem like you guys.
For me the problem was that my Wordpress Admin account was the same as Flarum account. In order to successfully sign in I had to delete all users in Flarum database which had the same email address or username.
To keep it short: WP user cant log in if there is a similar user already in Flarum database. Is that the way it's supposed to be @maicol07 ? Also, thank you for everything!