To answer this question, we need to know how the flow will be triggered.

If your flow is running on an automated trigger, then it will always run in the context of an owner of flow (The person who created the flow).

However, for the manually triggered flows, such as Flow Button, Flows added to Power Apps, SharePoint “For a selected item” and “For a selected file”, the flow can be configured to run in the context of the user who starts it. If the flow uses a premium connector then the person pressing the button needs to have a premium license. For a flow to run in the context of the user who starts it, the person invoking the flow must provide their connection (credentials). This is achieved through the Manager Run-Only Users section of the flow properties. This only appears on manual triggers.

  • Click on Add another user in the Manage Run-Only Users tile
    • Add the users with whom you’d like to share the flow.
    • In the Connections used section, click on the dropdown and configure it to be “Provided by run-only user” for the connections you want.