I don't know the answer to your question about how to use the Oracle.ManagedDataAccess control inside a Pro add-in. I'm not familiar with the control.
An alternate implementation you might consider is to use the Database class from the Pro SDK. This allows you to directly access relational databases that may or may not be ArcGIS geodatabases.
I have been using the Geodatabase class to access a feature class and get info. However, the performance is horrible!! I was hoping to use the Oracle.ManageDataAccess control to go straight against the database views and hopefully get better performance (this is what I have done in my ArcMap Add-Ins and the performance is great). I will look at the Database class but I assume it will be the same on a performance level.
When I say bad performance here is an example. I am looking up a subdivision by object id. In ArcMap it takes less than a second to locate and highlight the subdivision in the map - basically I click the OK button and it shows up. In Pro, it takes close to 3 seconds to highlight the subdivision in the map. It isn't just the subdivision feature class either, I have seen this same type of performance with other feature classes. I am currently drawing nothing in the map - just highlight the subdivision. In this example, I am not using the Oracle.ManagedDataAccess class I am using the Geodatabase class in Pro SDK or ArcObjects for ArcMap. I am experiencing the same slowness with other simple database type queries where I only want attribute info which is why I wanted to try the Oracle data provider. My preference is to stick with ArcGIS Pro SDK objects and controls.
Is this behavior typical? If so, I will move on, finish the code, and live with the poor performance. If not, I would like to build it right the first time.