To integrate Telegram into Twilio Flex Conversations, you need to create a Telegram bot and set up a new Studio Flow that routes incoming conversations from Telegram to Flex. The application will listen for events from Telegram when a new message is sent and send it to Twilio, as well as vice versa. This process requires backend development and no additional Flex UI plugin. After setting up the bot and flow, you can receive messages from Telegram and forward them to Flex Conversations using an HTTPS POST request. The application will create a conversation in Flex, add participants, and send messages between agents and customers. To complete the integration, you need to set up webhooks for both incoming and outgoing messages, allowing agents to reply to customers.