if i understand correct, The flow appears in "shared with me" even though its not shared with anyone and you are the owner of the flow?
The original way to share is the same way. you click on share icon and then you add users who can be added as owner.
If you want to share with run only permissions and your flow plan is "user who run the flow" you will see run only as well in your specific flow.
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Thanks,
Rahber
