@chiguypaul
Sorry - I misunderstood your question. If this is a Flow that starts with a Button, the only way a user to whom you have granted run-only permissions will be able to run the Flow is from a button on their phone or other mobile device. If it were a for a selected item Flow, it could be run from the browser when an item is selected.
If you want the user to run it from their browser, you could add them as an owner - they would see it under "Shared with me". Another alternative is to export the Flow or use the "Send a copy" feature. If you do that, the user can import the Flow and supply their own connection information.