I'm not sure if two separate applications are a good idea.
It seems that you will have enough duplication if you do so because I do not think the two applications will be mutually exclusive. At least I suppose that public parameters will also be available when the user logs in, right? This means that a good fragment of the public application, client and server should be part of a secure application. It is hard to maintain.
Also consider the user experience. The user will have to download the whole new application during login and logout, at least for the first time, until he gets into the browser cache. Depending on the size of your application, which may take several seconds to wait.
The standard approach is to have one Angular application and one Flask application. An Angular application starts and shows all available options, and depending on what the user is doing Angular, sends Ajax requests to Flask.
If the user is trying to do something that requires a login, then Flask will respond with a 401 code error. Angular can then display the login dialog to get the login credentials, and then send the Ajax request again, now with the credentials , possibly as basic HTTP authentication through secure HTTP. From now on, Angular can attach login credentials to all requests so that the user can now use all parameters.
If you do not want to send login information with each request, you can have the get_auth_token in your flash application, which takes the credentials and sends the token back to Angular. Angular can then attach the token to all subsequent requests.
The logout option in Angular then simply resets the credentials and / or token in order to become unauthorized again.
I explain some of these ideas in more detail in this answer . Although the context in this question was Node.js, the principles also apply to Flask.
You can also read my textbooks on this topic. I use Flask on the server and Knockout.js on the client, but the concepts should translate directly if you use Angular instead of Knockout. Here are three of them: