In the database in the post_meta table the meta_key (field name) of the flexible content field, the value stored is a serialized array of layout names.
If we were going to do a WP_Query using the meta value the meta_query would look something like this
meta_query = array(
array(
'key' => 'flex_field_name',
'value' => '"flex_layout_name"',
'compare' => 'LIKE'
)
)