Get public meta values in WP-API

gistfile1.php

function my_prepare_post( $post_response, $post, $context ) {
    $meta = get_post_custom( $post['ID'] );
    $custom_fields = array();
    foreach ( $meta as $key => $value ) {
        if ( '_' !== substr( $key, 0, 1 ) ) {
            $custom_fields[ $key ] = $value;
        }
    }
    $post_response['custom_fields'] = $custom_fields;
    return $post_response;
}
add_filter( 'json_prepare_post', 'my_prepare_post', 10, 3 );

this code in your plugin would add any custom field not starting with "_" to the response