Associate the "add_rewrite_endpoint" and "$_GET"

Query parameters added using add_rewrite_endpoint() are available using get_query_var().

So if you register /en/ as an endpoint:

function wpse_318560_en_endpoint(){
    add_rewrite_endpoint('en', EP_ALL);
}
add_action('init', 'wpse_318560_en_endpoint' );

And don’t flush rewrite rules on init. Rewrite rules only need to be flushed once. See this note in the developer docs for a way to properly flush rewrite rules programmatically.

Then you can use get_query_var() to check if the endpoint is present.

One important thing to note is that get_query_var returns the value of the query var. When adding an endpoint, the ‘value’ of the endpoint is whatever comes after the /en/ in the URL. In your use-case this will be an empty string: ''. The thing to be careful of is that the default value of get_query_var() when /en/ is missing is also ''.

So to properly check if /en/ is set in the URL, you need to use the 2nd argument of get_query_var() to change the default value to false:

// example.com/page/
get_query_var( 'en' );        // ''
get_query_var( 'en', false ); // false

// example.com/page/en/
get_query_var( 'en' );        // ''
get_query_var( 'en', false ); // ''

So to properly check for /en/ you need to do it like this:

if ( get_query_var( 'en', false ) !== false ) {

}

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