The process of deploying a Flask application (website and REST APIs) on Data Science & AI Workbench involves the following:
  1. Configuring Flask to run behind a proxy
  2. Enabling Anaconda Project HTTP command-line arguments
  3. Running Flask on the deployed host and port
Here is a small Flask application that includes the call to .run(). The file is saved to server.py. This Flask application was written using Blueprints, which is useful for separating components when working with a large Flask application. Here, the nested block in if __name__ == '__main__' could be in a separate file from the 'hello' Blueprint. 
from flask import Flask, Blueprint

hello = Blueprint('hello', __name__)

@hello.route('/')
def hello_world():
    return 'Hello, World!'

if __name__ == '__main__':
    app = Flask(__name__)
    app.register_blueprint(hello, url_prefix='/')

    app.run()

​
Running behind an HTTPS proxy

Workbench maintains all HTTPS connections into and out of the server and deployed instances. When writing a Flask app, you only need to inform it that will be accessed from behind the proxy provided by Workbench. The simplest way to do this is with the ProxyFix function from werkzeug. More information about proxies is provided here. 
from flask import Flask, Blueprint
from werkzeug.contrib.fixers import ProxyFix

hello = Blueprint('hello', __name__)

@hello.route('/')
def hello_world():
    return 'Hello, World!'

if __name__ == '__main__':
    app = Flask(__name__)
    app.register_blueprint(hello, url_prefix='/')

    app.wsgi_app = ProxyFix(app.wsgi_app)
    app.run()

​
Enabling command-line arguments

In your anaconda-project.yml file, you define a deployable command as follows: 
commands:
  default:
    unix: python ${PROJECT_DIR}/server.py
    supports_http_options: true
The flag supports_http_options means that server.py is expected to act on the following command line arguments defined in the Anaconda Project Reference. This is easily accomplished by adding the following argparse code before calling app.run() in server.py 
import sys
from argparse import ArgumentParser

# ... the Flask application blueprint

if __name__ == '__main__':
    # arg parser for the standard anaconda-project options
    parser = ArgumentParser(prog="hello_world",
                            description="Simple Flask Application")
    parser.add_argument('--anaconda-project-host', action='append', default=[],
                        help='Hostname to allow in requests')
    parser.add_argument('--anaconda-project-port', action='store', default=8086, type=int,
                        help='Port to listen on')
    parser.add_argument('--anaconda-project-iframe-hosts',
                        action='append',
                        help='Space-separated hosts which can embed us in an iframe per our Content-Security-Policy')
    parser.add_argument('--anaconda-project-no-browser', action='store_true',
                        default=False,
                        help='Disable opening in a browser')
    parser.add_argument('--anaconda-project-use-xheaders',
                        action='store_true',
                        default=False,
                        help='Trust X-headers from reverse proxy')
    parser.add_argument('--anaconda-project-url-prefix', action='store', default='',
                        help='Prefix in front of urls')
    parser.add_argument('--anaconda-project-address',
                        action='store',
                        default='0.0.0.0',
                        help='IP address the application should listen on.')

    args = parser.parse_args()

​
Running your Flask application

The final step is to configure the Flask application with the Anaconda Project HTTP values and call app.run(). Note that registering the Blueprint provides a convenient way to deploy your application without having to rewrite the routes. 
# ... the flask application blueprint

if __name__ == '__main__':
    # ... parse command line arguments

    app = Flask(__name__)
    app.register_blueprint(hello, url_prefix=args.anaconda_project_url_prefix)

    app.config['PREFERRED_URL_SCHEME'] = 'https'

    app.wsgi_app = ProxyFix(app.wsgi_app)
    app.run(host=args.anaconda_project_address, port=args.anaconda_project_port)
Here is the complete code for the Hello World application. 
import sys
from flask import Flask, Blueprint
from argparse import ArgumentParser
from werkzeug.contrib.fixers import ProxyFix

hello = Blueprint('hello', __name__)

@hello.route('/')
def hello_world():
    return "Hello, World!"

if __name__ == '__main__':

    # arg parser for the standard anaconda-project options
    parser = ArgumentParser(prog="hello_world",
                            description="Simple Flask Application")
    parser.add_argument('--anaconda-project-host', action='append', default=[],
                        help='Hostname to allow in requests')
    parser.add_argument('--anaconda-project-port', action='store', default=8086, type=int,
                        help='Port to listen on')
    parser.add_argument('--anaconda-project-iframe-hosts',
                        action='append',
                        help='Space-separated hosts which can embed us in an iframe per our Content-Security-Policy')
    parser.add_argument('--anaconda-project-no-browser', action='store_true',
                        default=False,
                        help='Disable opening in a browser')
    parser.add_argument('--anaconda-project-use-xheaders',
                        action='store_true',
                        default=False,
                        help='Trust X-headers from reverse proxy')
    parser.add_argument('--anaconda-project-url-prefix', action='store', default='',
                        help='Prefix in front of urls')
    parser.add_argument('--anaconda-project-address',
                        action='store',
                        default='0.0.0.0',
                        help='IP address the application should listen on.')

    args = parser.parse_args()

    app = Flask(__name__)
    app.register_blueprint(hello, url_prefix = args.anaconda_project_url_prefix)

    app.config['PREFERRED_URL_SCHEME'] = 'https'

    app.wsgi_app = ProxyFix(app.wsgi_app)
    app.run(host=args.anaconda_project_address, port=args.anaconda_project_port)