Hello @ChristinaD,
At this time, the function you are describing of using a flow to move customers from one list to another automatically is not supported. Customers are only added to a list automatically when your customers share explicit consent and sign up to the new list such as through a signup form connected to that new list.
Depending on what it is you were trying to accomplish, a workaround would be using an Update Profile Property step in your flow to tag your customers who have completed and/or removed from the flow through a conditional split. Through this strategy of tagging these customers who meet a conditional and are removed from a flow, you can capture these customers within a segment which can then be used as your recipient group along with your general email list when sending a campaign. You can learn more about using an update profile property action step from the Update Profile Property Action Use Cases and How to Add an Update Profile Property Action to a Flow articles.
Hope this helps!
David