Currently, a Flow with using a For a Selected Item trigger can be shared on a run-only basis with a SharePoint list. Users with Edit access to the list can see and execute the Flow. However, users with Contribute access cannot see the Flow in the Flow dropdown menu.
I suggest allowing users with Contribute access to see and execute For a Selected Item Flows. Many site admins change the permissions on the members group from Edit to Contribute immediately upon creating a site. The reason is that many believe that Edit access affords end users too much opportunity to make unwanted changes to lists.
Allowing users with Contribute access to run For a Selected item Flows will eliminate the need for site admins to choose between adequately securing their site and using For a Selected Item Flows.