If needing to do this in code for Framework 4.5, then it's perhaps worth knowing there are a couple of deprecated nuget packages that should allow you do the job.
Note: Deprecated in MS parlance means no longer in development.
Provided you have Set up the Vault, registered an App in Azure-AD, and granted access to the vault from the app, then it should essentially be a case of requesting a key-secret from the vault, using the app-name, app-key and key-name.