Exclude first 2 posts with meta_key from loop

First point is that you should NOT use query_posts() for custom queries. The better approach is to use the WP_Query class. More info in the WP docs and here.

This example will display your 2 featured posts and then exclude them in the second query.

// We will push the ID of your featured posts to this array
$excl_posts[] = '';

// Query arguments from your featured posts query
$feat_args = array(
    'posts_per_page' => '2',
    'meta_query' => array(
        array(
            'key' => 'featured_post',
            'value' => '1',
            'compare' => 'LIKE'
        )
    )
);

// Instantiate new WP_Query instead of using query_posts()
$featured = new WP_Query( $feat_args );

if ( $featured->have_posts() ):
  while ( $featured->have_posts() ):
    $featured->the_post();

    // Do stuff with each posts
    echo get_the_title() . "<br>";

    // Push current postID onto the exclude array
    $excl_posts[] = get_the_ID();
  endwhile;
endif;

wp_reset_postdata();

$excl_feat_args = array(
    'posts_per_page' => '10',
    'post__not_in' => $excl_posts,
    'meta_query' => array(
        array(
            'key' => 'featured_post',
            'value' => '1',
            'compare' => 'LIKE'
        )
    )
);
$excl_featured = new WP_Query( $excl_feat_args );

if ( $excl_featured->have_posts() ):
  while ( $excl_featured->have_posts() ):
    $excl_featured->the_post();
    echo get_the_title() . "<br>";
  endwhile;
endif;

wp_reset_postdata();