Cloning a Twilio Flex Project involves creating new environments by duplicating existing ones, ensuring regulatory compliance, and updating external assets, tools, and services. This process requires coordination with Twilio's support team to flag the new project for the correct level of support. The steps involve cloning Twilio Functions and Assets, recreating the Task Router Workspace, and connecting phone numbers to Studio Flows. Additionally, configuring Flex settings, deploying Flex plugins, and updating source code are necessary tasks in the process.