In the DB the flex field is stored as an array of layout names.
$flex_field_name = 'name of your flex field here';
$layout_name = "name of your layout here";
$args = array(
'post_type' => 'page',
'posts_per_page' => -1,
'meta_query' => array(
array(
'key' => flex_field_name,
'value' => '"'.$layout_name.'"'
'compare' => 'LIKE'
)
}
);