Run Flask alongside PHP [sharing session]

I'm not sure this is the answer you are looking for, but I would not try to have the Flask API access session data from PHP. Sessions and API do not go well together, a well designed API does not need sessions, it is instead 100% stateless.

What I'm going to propose assumes both PHP and Flask have access to the user database. When the user logs in to the PHP app, generate an API token for the user. This can be a random sequence of characters, a uuid, whatever you want, as long as it is unique. Write the token to the user database, along with an expiration date if you like. The login process should pass that token back to the client (use https://, of course).

When the client needs to make an API call, it has to send that token in every request. For example, you can include it in the Authorization header, or you can use a custom header as well. The Flask API gets the token and searches the user database for it. If it does not find the token, it returns 401. If the token is found, it now knows who the user is, without having to share sessions with PHP. For the API endpoints you will be looking up the user from the token for every request.

Hope this helps!