Manage Flows versus Run Flows permissions
Key Takeaway
Run Flows lets users run active flows, but only admins with the Manage Flow user permission can run inactive flows.
Being able to reach a flow and being allowed to run it are separate things. Which permission a user needs depends on whether the flow is active. Either way, the flow still needs the right object, field and record access to finish.
What a user needs to run flows
Putting a flow where users can reach it, such as on a Lightning page, does not mean they can run it. To run flows, a user needs either the Flow User permission on their user record or the Run Flows permission on an assigned profile or permission set.
Granting Run Flows through a profile or permission set is more efficient than granting it user by user, because it gives access to a whole group at once.
In Setup, Run Flows is an app permission, not a system permission. In a permission set, it is under App Permissions, in the Flow and Flow Orchestration section. In a profile, it is under General User Permissions.