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

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

From within the UI of your application, use an href or some javascript/jquery to open the window.  Since FlowWright requires authentication, authentication can be bypassed by passing authentication from your application to FlowWright.

Another way to perform authentication is to, use the FlowWright REST API and to get an authentication token, use this token to authenticate with the User interface.