There is no "New" button to create a blank canvas that would function as a separate flow. You can organize your flows into separate Process Groups, though. It's a visual distinction, and still subject to the policy hierarchy of Process Groups. Other parts of your flow can send and receive data between Process Groups via input and output ports. You can achieve what you're looking for by creating a Process Group and moving your existing flow into it, and then creating a second Process Group to create your "second flow".
Is there a 'New' button to start creating a new flow/template? I was only able to move the existing flow and start adding new processors for building a new flow but wondering if there is anything I'm missing to start with a new canvas to start building a new flow.