The 'READ-ONLY' status has nothing to do with the flow being locked or not. It means the version you are looking at is not the latest version of the flow. This happens because the parent flow, that the subflow block is referencing, is an older version of the actual flow.
For example, I have a flow that have several different versions created along the way. If I open the latest version of the Flow saved in the TDM Repository (version 18.104.22.168).
When I right-click on the subflow block, "Subflow_1", and select "Open Subflow in New Tab", the subflow opens as "READ-ONLY".
This happens because the parent flow is referencing an older version of the "Subflow_1" flow. Since you cannot edit older versions of a flow, it opens in read-only.
To get around this, you will need to open the most recent version of the subflow, by going to the "Manage" tab and click the "Revision History" button.
The Revision History dialog window will open. Select the "Load Version" button to open the most recent version of the flow.
Which will open the most recent version of the flow, and allow you to make your edits.