@app.before_request
def requests_session():
    flask.g.requests_session = requests.Session()
    # Do more configuration based on app.config["REQUESTS"] for example

import threading

import requests


class RequestsSessionRegistry(object):

    def __init__(self, session_factory=None):
        self.registry = threading.local()
        if session_factory is None:
            self.session_factory = requests.Session

    def __call__(self, *args, **kwargs):
        """
        Create or get the current thread-local requests session
        """
        if not hasattr(self.registry, 'session'):
            self.registry.session = self.session_factory(*args, **kwargs)
        elif args or kwargs:
            # args or kwargs can't be provided if there's already a session
            raise ValueError('args and kwargs must be none if the registry has'
                             ' a session already. Call `remove` first.')

        return self.registry.session

    def remove(self):
        """
        Close all open connections and remove the thread-local session.
        """
        if hasattr(self.registry, 'session'):
            self.registry.session.close()
            del self.registry.session

# Done at the module level, everyone just imports this Session
RequestsSession = RequestsSessionRegistry()

session = RequestsSession()
session.get('http://example.com')