Currently, the only people who can view Flow Run information are named Owners of a Flow (that is, individual users, not Groups or SharePoint sites, lists or libraries set as Run-Only users). To provide equivalent functionality to SharePoint Designer workflows, any user who initiates a Flow (manually ["for a selected item" or from a button] or via a PowerApps action) should be able to view the progress ("Run") of that Flow.
I understand that Flow is in many ways meant to be a personal service with users creating and managing their own processes, but the reality is that in most organizations, creating Flows continues to be an "IT" function. As such, IT departments should be able to create and deploy Flows in a manner that allows business users to run and monitor them as needed. The only way to do this now is to add another named user as an Owner, which also gives them access to edit the Flow (which is often unnecessary and risky).