Have you had experience connecting external databases to a Flask application?

Yes, connecting external databases to a Flask application is a common task. Usually, an ORM like SQLAlchemy is used, or drivers for specific databases.

Example of connecting to a PostgreSQL database using Flask and SQLAlchemy:

from flask import Flask
from flask_sqlalchemy import SQLAlchemy

app = Flask(__name__)
app.config['SQLALCHEMY_DATABASE_URI'] = 'postgresql://user:password@localhost/dbname'

db = SQLAlchemy(app)

class User(db.Model):
    id = db.Column(db.Integer, primary_key=True)
    username = db.Column(db.String(80), unique=True, nullable=False)

# Usage:
# user = User.query.filter_by(username='example').first()

Thus, you configure the connection string, and SQLAlchemy manages interaction with the database. You can also use pure drivers, such as psycopg2 for PostgreSQL, if ORM is not needed.