Twilio Flex 2.0 allows users to configure Facebook Messenger with Flex Conversations, enabling two-way messaging between customers and agents. To set up this integration, users need to install and configure the Facebook Messenger channel, create a Studio flow, and then create a Conversations address. The process involves linking a Facebook page to Twilio, creating a new flow in Studio, and specifying the TaskRouter workflow and chat channel. Once these steps are completed, users can verify their setup by running a command with the Twilio CLI and see their Conversations address created. With this integration, users can start receiving messages from Facebook Messenger users and respond as Flex agents, enabling two-way conversation between customers and agents.