In your cloud flow, if you have the action "Respond to a Power App or a Flow", the app or the flow from where this flow was triggered, is basically waiting for a response. If the flow errors out, it automatically goes into retry mode which is why you see the auto trigger in the flow if an instance has failed.
In the flow, you can implement error handling and return a value to the Power App even if the desktop flow has failed. Based on the variable action then, you can show an error or success message to the user. This will prevent the flow from going into retry logic and auto triggering.
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