maicol07 I have implemented this extension today on a Wordpress site that has a Flarum instance on the same domain but within a subfolder, so the main site is at www.example.com and the Flarum instance is at www.example.com/forum
I have also enabled the options to remove register and login links from Flarum, excellent addition, thanks.
When logging into my main site, via Wordpress login, the user is successfully logged into Flarum. Awesome.
Logging out from Flarum does successfully direct the user to the logout screen in Wordpress, where presently there is a confirmation "Do you really want to log out" which I am hoping it's possible to code around and make the log out just happen without the confirmation.
However, I am finding, as @lubos-h reports, that logging out through Wordpress does not log the user out of Flarum.