How do I add my PHP app to a WordPress page whilst keeping semantic URLs?

Its not good way to edit .htaccess for wordpress url rewriting (only for main urls settings from admin panel)

You found your response here : API basic url rewriting or The Rewrite API: Post Types & Taxonomies

An example :

add_action( 'init', 'rewrite_rule' );
function rewrite_rule()
{

  global
  $wp,$wp_rewrite;

  // Remember to flush the rules once manually after you added this code!
  add_rewrite_rule(
      // The regex to match the incoming URL
      'yourpage/([a-z0-9-]+)/?',
      // The resulting internal URL: `index.php` because we still use WordPress
      // `pagename` because we use this WordPress page
      // `designer_slug` because we assign the first captured regex part to this variable
      'index.php?pagename=yourpage&your_param=$matches[1]',
      // This is a rather specific URL, so we add it to the top of the list
      // Otherwise, the "catch-all" rules at the bottom (for pages and attachments) will "win"
      'top' );
  $wp_rewrite->flush_rules();
}

add_filter( 'query_vars', 'query_vars' );
function query_vars( $query_vars )
{
  $query_vars['yp'] = 'your_param';
  return $query_vars;
}

You get data : $param_website_name = $wp->query_vars['your_param'];

i hope that help you 😉