The DbContext instance that you create and can be retrieved using HttpContext.GetOwinContext().Get<ApplicationDbContext>();
within your MVC application can be left exclusively for the use of Identity Framework.
If you need an instance of your DbContext for general use within your application, you can make use of an IoC Container (dependency injection) to provide you with a fresh instance of it as an when required and in request scope if desired.
You shouldn't need to retrieve the identity framework instance of the DbContext for the use within your application, it will be managed independently of your application and you can manage your own lifecycle.
Because you wired these up within the Owin Startup class to use an instance of your DbContext, they will make use of it under the hood and will create and destroy instances as and when it is required.