The themes on AMP are detected from the plugin header which has a specific attribute.
For example in amp-theme.php we have:
Plugin Name: AMP Theme Framework
Plugin URI: https://wordpress.org/plugins/accelerated-mobile-pages/
Description: Create AMP Themes easily with help of AMP Framework
Author: AMPforWP Team
Author URI: http://ampforwp.com/amp-theme-framework
In the above code, you can see the line number 9 which mentions the name of the AMP theme, this is a required if you are creating an AMP Theme.
When you add this line, then AMPforWP will automatically detect it as a theme and display it in the Dropdown menu of the design selector (under AMP > Appearance > Themes > Themes Selector ). See the screenshot
When you select the theme from this dropdown and save it then it will start working.