Process designer can be opened using the direct URL and by passing a process definition id:

http://localhost/cDevWorkflow/deDesignWorkflow.aspx?defID=xxxxxxxxxxxxxx

From within your application's UI, use an href or some Javascript/JQuery to open the window. Since FlowWright requires authentication, you can bypass it by passing authentication from your application to FlowWright.

Another way to authenticate is by using the FlowWright REST API to get an authentication token. This token can be used to authenticate with the user interface.