Fans can subscribe to your Facebook page with a Signup Form.
To get started you need
A Plus plan subscription. If you're unsure what your subscription includes, please contact your account manager or firstname.lastname@example.org
Connect a Facebook page first
Create a list for your Facebook Messenger subscribers to populate to
How to collect Facebook Messenger subscribers with a Signup Form
Follow these steps to create a Signup Form
Be sure to tick the Facebook Messenger channel
Add the form to your website and start collecting subscribers to direct message.