How to allow users to write jetpack custom post types? [closed]

No need to use Jetpack Post Types feature for that. Just use the following code to enable Jetpack Plublicize for any custom post type of your theme/plugin. Place it in functions.php:

 * Enable Jetpack Publicize Support for CPT
 * --------------------------------------------------------------------------
function wpse20150812_jetpack_publicize_support() {
    add_post_type_support( 'mycpt', 'publicize' );
add_action('init', 'wpse20150812_jetpack_publicize_support');

Replace the mycpt with your registered Custom Post Type.

Reference: – Support