Ok, so you are hoping that clicking the link in the app will log them in to your moodle site, and they'll be viewing your page with an active user session?
Doing this using custom menu items in your Moodle site settings isn't going to work, since the link wont log them in to your moodle site. We have a plugin that does something similar to display a user feedback form. Unfortunately it's not public so I can't point you to the code, but it uses a CourseMainMenuDelegate to display the menu item, then displays the form in the app. The db/mobile.php looks a bit like this:
$addons = [
'local_yourplugin' => [
'handlers' => [
'oufeedback' => [
'displaydata' => [
'title' => 'titlestring',
'icon' => 'text',
'class' => ''
'delegate' => 'CoreMainMenuDelegate',
'method' => 'mobile_yourplugin_view',
'offlinefunctions' => 
The mobile_yourplugin_view template function in classes/output/mobile.php then returns the template for the form, which is displayed in the app.
Another approach, if you're using basic Moodle authentication (not SSO) and you actually want to send the user to your moodle site rather than using the app, would be to create an autologin link in the app. This uses their web service token from the app to create a Moodle session for them so they will be logged in. Have a look at the documentation for the core-link directive.
If you are trying something like this and getting errors, please let us know what the errors say and when they appear.